aptitude

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Focus Academy for Career Enhancement

REFRESHER HANDOUT

Contents

Quantitative Ability Page

1. Numbers 2

2. Time and Work 5

3. Time, Speed and Distance 8

4. Percentages 11

5. Permutations and Combinations 13

6. Geometry 15

Logical Ability

1. Clocks and Calendars 19

2. Syllogisms and Logical Connectives 21

3. Data Interpretation & Data Sufficiency 25

4. Data Arrangement & Blood Relations 29

Verbal Ability

1. Sentence Correction 32

2. Sentence Completion & Para jumbles 33

3. Vocabulary 35

The Refresher handout is a quick revision of all the basic concepts covered in the Odd

semester. A set of sample practice questions are given at the end of each concept

which will give you the best direction for the preparation.

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NUMBERS

CONCEPT 1- BASICS

HCF and LCM

HCF – Highest common factor and LCM- Lowest common factor

HCM – Highest common multiple and LCM- Lowest common multiple

Ex.1 Find the HCM and LCF of 55, 125, 225.

The highest common multiple of any set of numbers is Infinity.

The least common multiple of any set of numbers is always 1.

Ex.2 Find the HCF of first 350 co primes.

The HCF of co primes is always 1.

NUMBER OF ZEROS IN n!

In order to obtain a zero, the requirement is 5 and 2.

Calculate the number of 2’s and 5’s and pair them up.

The number of zeros will be the number of pairs obtained.

Ex: Find the number of zeros in 50!

The no of 2’s will be greater than the number of 5’s.

Thus in order to pair up, it is sufficient if we find the no of 5’s.

50/5 gives ten 5’s and 10/5 gives two 5’s

Hence total no of 5’s = (10+2) = 12

Successive Division:

Ex: When a number is divided by 3 and 5, the remainder obtained is 1 and 2

respectively. What is the remainder is the number is divided by 15?

Divisor Remainder

3 1

5 2

Ignore 5, multiply diagonal and add horizontal.

So (3*2) + 1 gives 7. Hence the remainder is 7.

Concept 2: Digital Root Method

Whatever the operation is, proceed by calculating the sum of digits in the number and keep adding the

resulting sum until one digit remains.

Ex 1: 8216 X 4215 =?

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a. 34631440 b. 34631444 c. 34630440 d. 34630451

Here, 8+2+1+6= 17 => 1+7=8

4+2+1+5= 12 => 1+2=3

Digital root of the resultant product= 8 X 3= 24 =>6

The only option with digital root 6 is option c

Ex 2: Find the simple interest on a principle of Rs.123456789 for at the rate of 11% for a period of

7 years.

a. 9506172753 b. 9506182753 c. 9507774536 d. 9501256621

SI= Pnr /100 => Pnr/1 (Since Digital root of 100 is 1)

SI=123456789 X 11 X 7 => 9 x 2 x 7 => 126 => 9

[1+2+3+4+5+6+7+8+9 = 45 => 4+5=9]

Only option that has the digital root of 9 is option a

Concept 3-Remainder Theorem

Positive Remainder and Negative Remainder

When 5 is divided by 4, Positive Remainder is 1 and Negative Remainder is -3

Remainder when divisor is 3, 9 or 11

When a number to be divided by 3 or 9 is given, the remainder will be the digital

root of the number divided by the divisor

Ex: What is the remainder when 7280 is divided by 9?

7+2+8 = 17 => 8

In case of 11, the remainder is the difference of alternate numbers

Ex: What is the remainder when 1763891 is divided by 11?

(1+6+8+1)- (7+3+9) = -3 (or) 8

Finding Remainder for Product of Numbers

When a product of 2 or more numbers is given, find the positive or negative

remainder for each number and multiply them and then find the remainder for the

resulting product.

Ex 1: Find the remainder when 1349 x 1350 x 1351 is divided by 13.

Solution:

1349 % 13 = 10 (or) -3

1350 % 13 = 11 (or) -2

1351 % 13 = 12 (or) -1

Hence the remainder is -1 x -2 x -3 => -6 or 7

Finding Remainder for Powers

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When a number with an incalculably long power is given, convert the number in

terms of reminder and reduce the power such that in each subsequent step a smaller

remainder is obtained

Ex 1: Find the remainder when is divided by 18

Solution:

359 % 18= 17 (or) -1

The remainder is = 1

Practice Exercise

1. Three bells ring together at the equal intervals of 8, 10, 12 min respectively and they start

together at 8.00 am. What time will they ring together again?

a. 9.00am b. 10.00 am c. 10.30 am d. 9.45 am

2. Find the number of zero’s in 200!

a. 48 b. 49 c. 197 d.196

3. Find the LCM and HCF of 7, 11, 33

a. 231,1 b. 132,1 c. 231,7 d.132, 7

4. Find the 50th term in the series 2, 5, 8, 11…..

a. 149 b.144 c.150 d.148

5. A number when successively divided by 3, 5, 8 leaves remainders 1, 4, 7 respectively. Find

the respective remainders when the divided by 8, 5, 3.

a. 6, 4, 2 b. 6, 4, 3 c.2, 4, 6 d. 6, 3, 4

6. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same

remainder in each case. Then sum of the digits in N is

a. 4 b. 5 c. 8 d. 9

7. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater

number is:

a. 111 b. 101 c.37 d. 185

8. Find the remainder when (2561 x 2562 x 2563) / 11

a. 0 b. 1 c. 2 d. 3

9. Find the remainder when is divided by 17

a. 5 b. 1 c. 16 d. 4

10. Find the unit digit of the value( + )

a. 2 b. 3 c. 4 d. 5

11. Find the remainder when (2! + 3! + 4! + … + 20!) is divided by 4!

a. 6 b. 7 c. 8 d. 9

12. What is the remainder when is divided by 17?

a. 16 b. 17 c. 1 d. 0

13. What is the remainder when is divided by 40?

a. 0 b. 1 c. 2 d. 3

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14. A two digit number is formed by subtracting 2 from 5 times the sum of its digits or adding 14

to 9 times the excess of the unit digit over the tens digit. Find the two digit number.

a. 45 b. 56 c. 23 d. 34

15. The product of 5 consecutive numbers is always divisible by

a. 4! X 3 b. 2 X 5! c. 20 d. 5!

16. Find the digital root of 123456….4950

a. 6 b. 7 c. 8 d. 9

17. Find the remainder when 145723692 is divided by 9

a. 4 b. 1 c. 3 d. 2

18. Find the amount for 2 years in compound interest if the principle value is 2000, rate of

interest is 12 % per annum.

a. 2503.4 b. 2508.8 c. 2612.8 d. 2524.8

19. Find 143198172 x 1834

a. 262625447448 b. 266217289014

c. 262643472448 d. 262612573528

20. Find the number of factors in 750 excluding (1 and 750).

a. 14 b. 15 c. 18 d.32

Key:

1 B 11 C

2 B 12 C

3 A 13 A

4 A 14 C

5 A 15 D

6 A 16 A

7 A 17 C

8 A 18 B

9 D 19 A

10 B 20 A

Time and Work

Concept 1 – LCM Method

To solve questions by LCM method, first assume the total work as the LCM of given values

for easy calculation.

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Ex: A, B and C can do a piece of work in 10, 12 and 15 days respectively. If A starts to do

the work and if he is assisted by B and C on every third day, then on which day will the

work be completed?

Total work = LCM (10, 12, 15) = 60 units.

A = 6U/day; B = 5U/day; C = 4U/day

Everyday 6units will be completed and on every third day 15units will be completed.

Word done for 6 days = 4*6 + 2 * 15 = 54U

Next day A will complete the remaining 6units. So number of days = 7.

Concept 2 - Pipes and Cisterns

Here, assume the capacity of tank as the LCM of given values.

Ex: Pipes A and B are inlet pipes while pipe C is an outlet pipe. Pipe A fills a tank at 9000

litres /hour. B fills the tank in 2 hours while C can empty the tank in 4 hours. The tank gets

filled in an hour when all three are opened simultaneously. What is the capacity of the

tank?

Let the capacity of tank be LCM (2, 4, 1) = 4 litres.

For the assumed capacity,

B = 2litres/hr; C= (-1) litre /hr; A+B+C = 4litre/hr. Therefore, A= 3litre/hr

When A fills 3L/hr, tank capacity = 4L

Therefore when A fills 9000L/hr, tank capacity = 12000L

Concept 3 - Work Equivalence

The relationship between various factors involved in doing a work viz., men(N), days(D),

hours(H) and work(W) is given by chain rule as follows

=

Ex 1: 24 persons can construct a wall in 12 days, working 8 hours a day. In how many days

will 16 persons, working 6 hours a day, complete half the work?

Solution:

=

= 12 days.

Ex 2: A contractor is asked to do the work of laying cables that requires 20 men to work

for 30 days. They start the work and 10 days later, the deadline was advanced by 10 days.

How many more men would the contractor have to hire to complete the work on

schedule?

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20 men finish the work in 30 days, thus total work = (20*30)600 units

After 10 days, the deadline was advanced by 10 days. So the total number of days is 10 less

than 30, which is 20. Now 20 men work for 10 days initially. Thus (20*10) = 200 units of

work is being done. Now the remaining work is (600-200) = 200 units. This 400 units of work

must be done in 10 days. Thus no of men required will be (400/10) = 40 men. Hence 20

extra men are needed more to finish the work.

Practice Exercise

1. A can do a piece of work in 8 hours . A and C together can do it in just 4 hours, while B and C

together need 6 hours to finish the same work. In how many hours can C alone complete

the work?

a. 6 b. 8 c. 10 d. 4

2. Ram, who is half as efficient as Ravi, will take 24 days to complete a work if he worked

alone. If Ram and Ravi worked together, how many days will they take to complete the work

a. 4 b. 8 c. 10 d. 12

3. Machine P can print one lakh books in 8 hours. Machine Q can print fifty thousand books in

5 hours and machine R can print twenty five thousand books in 3 hours. All the machines

started printing at 8 a.m. Machine P is stopped at 10 a.m. and the remaining two machines

complete work. At what time will the printing of one lakh books be completed

approximately?

a. 11a.m. b. 12 p.m. c. 1p.m. d. 2 p.m.

4. The HOD of JNT classes can prepare a question paper in 15 days, while each of his two

assistants can prepare a similar question paper in 20 days. JNT has to prepare a series of 20

such papers. The three member team plan to complete the work together. How long would

this three member team take to complete the task?

a. 100 b. 120 c. 140 d. 180

5. Three pipes A,B and C can fill a tank in 10,12 and 15 hours respectively. Find the time taken

to fill the tank, if pipe C is kept open all the time and pipes A and B are opened for each

alternatively starting with A.

a. 3

b. 6

c. 2 d. 4

6. There are two pipes A and B. Pipe A is a filling pipe and pipe B is an emptying pipe. Pipe A

can fill the tank is 7 hours and pipe B can empty the tank is 6 hours. If both the pipes are

open simultaneously then after how many hours will the tank be full?

a. 42 b. 7 c. 6 d. cannot be filled

7. 3 men or 5 women can do a job in 12 days. How long will 9 men and 5 women take to finish

the job?

a. 2 b. 3 c. 3

d. 4

8. There are 3 groups of workers, A, B, and C. In each group, all the workers work at the same

rate. Five workers of group A or 8 of group B or 10 of group C can build a wall in 3 days. If

this job is given to a group of 5 workers, 1 from A, 1 from B and 3 from C, how long would

they take to build the wall?

a. 6 b. 8 c. 6

d.

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9. A fills the tank in 30 hours and B empties the tank in 15 hours. Find the time taken (in hours)

by A and B working together to empty the tank (Assuming tank to be full at the start).

a. 15 b. 20 c. 25 d. 30

10. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3

gallons per minute. All the three pipes working together can fill the tank in 12 minutes. The

capacity of the tank in gallons is

a. 120 b. 240 c. 360 d. 480

Key:

1 B 6 D

2 B 7 B

3 B 8 D

4 B 9 D

5 B 10 C

TIME, SPEED AND DISTANCE

Concept 1: Average Speed & Relative Speed

If the speed of onward journey is x kmph and that of the return journey is y kmph, the average speed of the total journey is, 2xy/(x+y)

When two objects A and B are travelling at speeds of SA and SB, the formula for relative speed,

When travelling in the same direction = SA - SB

When travelling in the opposite direction = SA + SB Examples:

1. Raj lives 120 km away from Ram’s place. Both of them are travelling towards each other. Raj is travelling in his bike at a speed of 20 kmph and Ram is travelling at a speed of 40 kmph. After how much time will they meet each other?

Since opposite direction, Relative Speed = SA + SB

= 20 + 40 = 60 kmph

Time taken = 120 / 60 = 2 hours

Concept 2: Problems based on Trains Trains crossing stationary objects

Time taken by a train of length l metres to pass a pole is equal to the time taken by the train to cover l metres.

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Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.

Examples:

1. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Speed of the train relative to man =

125

m/sec 10 = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Concept 3: Problems based on Boats and Streams

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then: Speed downstream = (u + v) km/hr. Speed upstream = (u - v) km/hr.

If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = 1

(a + b) km/hr. 2

Rate of stream = 1

(a - b) km/hr. 2

Examples:

1. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Speed downstream = (5 + 1) kmph = 6 kmph. Speed upstream = (5 - 1) kmph = 4 kmph. Let the required distance be x km.

Then, x

+ x

= 1 6 4 2x + 3x = 12 5x = 12 x = 2.4 km

Concept 4: Problems based on Races

Circular Tracks If two runners start at the same time and from the same point and run in the same

direction, when they meet for the first time, the faster runner would have run one round more than the slower runner.

Time taken for the first meeting = Length of the track / Relative Speed of runners

Example:

1. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

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A : B = 100 : 75 B : C = 100 : 96.

A : C =

A x

B

=

100 x

100

= 100

= 100 : 72. B C 75 96 72

A beats C by (100 - 72) m = 28 m.

2. In a circular race of 1200 m, A and B start from the same point and at the same time with speeds of 27 kmph and 45 kmph. Find when will they meet again for the first time on the track when they are running in the same direction and opposite direction (in seconds)?

Length of the track, l = 1200 m Speed of A = 27 × 5/18 = 7.5 m/s Speed of B = 45 × 5/18 = 12.5 m/s

(i) Same direction

Time = l / Relative Speed = 1200/(12.5−7.5) = 240 sec

(ii) Opposite Direction Time = l / Relative Speed = 1200/(12.5+7.5) = 60 sec

Practice Exercise:

1. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

a. 120 m b. 240 m c. 300 m d. None of These

2. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

a. 3.6 sec b. 18 sec c. 36 sec d. 72 sec

3. Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

a. 2:3 b. 4:3 c. 6:7 d. 9:16

4. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

a. 2:1 b. 3:2 c. 8:3 d. Cannot be determined

5. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

a. 16 hours b. 18 hours c. 20 hours d. 24 hours

6. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

a. 4 km/hr b. 6 km/hr c. 8 km/hr d. Data Inadequate

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7. A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him

by 8 seconds. The speed of B is: a. 5.15 kmph b. 4.14 kmph c. 4.25 kmph d. 4.4 kmph

8. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

a. 8 points b. 10 points c. 14 points d. 40 points

9. Two athletes cover the same distance at the rate of 10 kmph and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.

a. 750 km b. 7.5 km c. 7.5 m d. 15 km

10. In a 400 m race, A gives B a head start of 50 m and wins by 20 seconds and if A gives a head start of 90 m, the race ends in a dead heat. What will be the time taken by A to complete the race?

a. 200 s b. 77.5 s c. 155 s d. 86.5 s

Answer Key:

1 b.

2 c.

3 b.

4 c.

5 d.

6 b.

7 b.

8 b.

9 b.

10 c.

Percentages

General calculations of percentage which is focussed on solving 10% of the problem.

Ex: 20% of 40 =8

Always a% of b = b% of a

Ex: 82% of 150= 150% of 82

Therefore, 150% of 82 = 123

Concept 1-Percentage Increase or Decrease

If increase is 1/n, then decrease should be 1/(n+1)

Ex 1. Price of pen has been increased from 30 to 35, what is the percentage increase in the

price?

Percentage increase = (change/base value) * 100

= (5/30)*100

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= 16.66%

Ex 2. The price of sugar has been increased by 25%, by what percentage should I reduce

my consumption so not to increase my expenditure?

Price of the sugar is increased by 25% = ¼(1/n)

Therefore the decrease should be 1/5(1/n+1) = 20%

Concept 2-Successive Increase or Decrease:

If initial increase was a% and successively a%, Total increase = a + b + (ab/100)

Ex 1. The length of rectangle is increased by 10% and breadth increased by 15%.Find the

effective increase in the area of rectangle?

The effective increase in area = 10 + 15 + (150/100) = 26.5%

Concept 3-Simple Interest

Ex 1. Find the simple interest for 7000 at rate of interest 5% for 2 years?

Simple Interest = 10 %( 7000) = 700

Ex 2. In simple interest, a sum becomes four times of itself in 20 years. Find the rate of

interest?

Assume principle = 100, therefore, interest = 300

Rate of interest = 300/20 = 15%

Concept 4-Compound Interest:

Ex 1. Find the compound interest on 20000 at 5% per annum in 2 years?

N=1, Interest = 5% of 20000 = 1000

N=2, Interest = 5% of 21000 = 1050

Total interest = 1000+1050 = 2050

Ex 2. A person borrowed Rs. 1000 at 20% per annum simple interest and immediately lent

it to another person at the same rate of interest for compound interest. Find the profit

obtained by him at the end of 2 years?

Simple interest = 40% of 1000 = 400

Compound interest = 200 + 20% of (1000+200)

= 440

Profit = 40.

Practice Exercise

1. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be

obtained from 100 kg of fresh fruits?

a. 40 b. 50 c. 70 d. 30

2. In an election between two candidates, one got 55% of the total valid votes, 20% of the

votes were invalid. If the total number of votes was 7500, find the number of valid votes

that the other candidate got?

a. 3400 b. 2700 c. 2500 d. 2400

3. Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If

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he paid Rs.686 as interest at the end of the loan period, what was the rate of interest?

a. 6% b. 9% c. 8% d. 7%

4. A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.c.p.a. in 5 years. What is

the sum?

a. 2412 b. 2332 c. 2323 d. 2233

5. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs.

1600 each on 1st January and 1st July of a year. At the end of the year, the amount he

would have gained by way of interest is

a. 111 b. 144 c. 121 d. 131

6. The difference between simple and compound interests compounded annually on a certain

sum of money for 2 years at 4% per annum is Re. 1. The sum is

a. 600 b. 525 c. 725 d. 625

7. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average

percent increase of population per year is

a. 4% b. 5% c. 6% d. 7%

8. A sum of money was put at SI at a certain rate for 2 years. Had it been at 1% higher rate, it

would have fetched Rs 24 more. Find the sum.

a. 1200 b. 1500 c. 1700 d. 1000

9. What is the capital required to earn a monthly interest of Rs 600 at 6% per annum?

a. 100000 b. 120000 c. 150000 d. 200000

10. If a certain sum at simple interest amounts to Rs 1260 in 2 years and Rs 1350 in 5 years, find

the rate and principle?

a. 2.5% b. 3% c. 3.5% d. 4%

Key

1 A 6 D

2 B 7 B

3 D 8 A

4 C 9 B

5 C 10 D

Permutation, Combination and Probability

Concept 1-Permutation

If there are n items we can arrange them linearly in n! Ways

Ex 1. In how many ways can the letters of the word 'LEADER' be arranged?

The word 'LEADER' contains 6letters, namely 1L, 2E, 1A, 1D and 1R.

Required number of ways = 6! = 360.

(1!)(2!)(1!)(1!)(1!)

Ex 2. Find the 51th rank, when you arrange the given letters in the word MANGO in an

nPr = n! / (n-r)!

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alphabetical order.

MANGO ----- Alphabetical order A, G, M, N, O

A 4! Ways = 24

G 4! Ways = 24

M A G 2! Ways = 2 50th rank

M A N G O 51th Rank

Concept 2-Combination:

Co

Ex 1. 10 points where none of them are collinear, by using these points how many triangles can

be formed?

We can form a triangle by connecting any three lines, out of 10.

Hence 10C3

Ex 2. In how many ways can a group of 9 persons be divided into 3 groups of sizes 3,2 and 4

each?

(Total no of players)! = 9!

(Each Team size)! × (no of teams)! (3! × 2! × 4!)×3!

Concept 3: Probability

Ex 1. A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.

The probability that first toy shows the even number =10/21

Hence, probability that second toy shows the even number = 9/20

Required probability = (10/21) × (9/20)= 9/42

Ex 2. An urn contains 6 red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?

P (None is blue) = 8C3/13C3 = 56/286 = 28/143 P (At least one is blue) = 1 − 28/143 = 115/143

Practice Exercise:

1. How many different four letter words can be formed (the words need not be meaningful)

using the letters of the word “MEDITERRANEAN” such that the first letter is E and R?

a. 59 b. 11! / (2! 2! 2!) c. 56 d. 23

2. What is the probability that the position in which the consonants appear remain unchanged

when the letters of the word Math are re-arranged?

a. 1/4 b. 1/6 c. 1/24 d. 1/12

nCr = n! / (n-r)! r!

P (A) = Favourable event / Total event = n (A) / n(S)

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3. A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the

number of ways of selecting the balls of different colours?

a. 62 b. 48 c. 12 d. 24

4. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?

a. 120 b. 720 c. 729 d. 125

5. In how many ways can you arrange the letters given in the word “MISSISSIPPI”?

a. 34650 b. 11! / (4! 4!) c. 11! d. 34000

6. A conference is attended by 30 participants. If each participant shakes hand with every

other participant, what will be the resultant number of handshakes?

a. 25 b. 300 c. 276 d. 325

7. In how many ways can 5 members be selected from a group of 8, such that one member is

always selected?

a. 45 b. 35 c. 20 d. 120

8. What is the sum of all the 4 digit numbers that can be formed using all the digits 2, 3, 5 and

7?

a. 113322 b. 11322 c. 11332 d. 113332

9. How many diagonals does a decagon have?

a. 45 b. 35 c. 90 d. 70

10. The letters of the word “ENGAGEMENT” are arranged such that all the vowels are together.

How many such arrangements are possible?

a. 7! × 4 / (3! 2! 2!) b. 10! / (3! 2! 2!)

c. 7! / (3! 2! 2!) d. 7! × 4 / (2! 2!)

Key

1 A 6 B

2 A 7 B

3 D 8 A

4 C 9 B

5 A 10 D

Geometry

Concept 1: Areas

Distance covered in 1 revolution = Circumference of the wheel = 2πr. Area of path = 2 x Width x [Length + Breadth + (2 x Width)]

1. The diameter of the wheel of a vehicle is 5 metre. It makes 7 revolutions per 9 seconds. What is speed of the vehicle in km/h?

a. 44 km/h b. 24 km/h c. 48 km/h d. 40 km/h

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Solution: Radius of the wheel = 52 metre Distance covered in 1 revolution = Circumference of the wheel = 2πr = 2 x 227×52 metre Therefore, Distance covered in one second = 2 x 227×52×79 metre Therefore, Speed per hour = 2 x 227×52×79×185 = 44 km/h option a 2. A field is 40 metre long and 35 metre wide. The field is surrounded by a path of uniform width of 2.5 metre runs round it on the outside. Find the area of the path.

a. 480 m2 b. 420 m2 c. 440 m2 d. 400 m2 Solution:

Area of path = 2 x Width x [Length + Breadth + (2 x Width)] = 2 x 25 x (40 + 35 + 2 x 2.5) = 5 x (75 + 5) = 400 m2 option d

Concept 2: Volumes and Surface Areas 1. The length of the wire of 0.2 mm radius that can be drawn after melting a solid copper sphere of diameter 18 cm is:

a. 24400 m b. 24380 m c. 44300 m d. 24300 m Solution: Radius of sphere = 9 cm Volume of sphere = [4/3×π(9)3]cm3=(972π)cm3 = 1/50 cm Let the length be = x cm Then, 972π=π×(1/50)2×x ⇒x=(972×50×50) cm Length of wire = (972×50×50)/100 m = 24300 m Option d 2. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8cm×6cm×2cm, is :

a. √26 cm b. 3√26 cm c. 2√26 cm d. 4√26 cm Solution: Length of pencil = √(8)2+(6)2+(2)2 cm = √104 cm = 2√26 cm option c

Concept 3: Mensuration

1. If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is

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a. 1/2w b. c c. d. Solution: The area of triangle ABD is half the area of triangle ABC. Both triangles have the same base AB. So, the altitude BD of triangle ABD is half the altitude BC of triangle ABC. So, z = y. Now, AD is the hypotenuse of the triangle ABD.

So, AD = .... exp (1) In triangle ABC, AC2 = w2 = x2 + (y + z)2 But y = z, so we can rewrite the expression as w2 = x2 + (y + y)2 Or w2 = x2 + 4y2 Or x2 = w2 - 4y2

Substituting this value of x2 in exp (1), we get option d

Practice Exercise

1. Four horses are tethered at 4 corners of a square field of side 70 meters so that they just cannot reach one another. The area left un-grazed by the horses is: a. 1050 sq.m b. 3850sq.m c. 950sq.m d. 1075 sq.m

2. A square sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of the base radius to the side of the square?

a. b. c. d.

3. The surface area of the three coterminous faces of a cuboid are 6, 15, 10 sq.cm respectively. Find the volume of the cuboid.

a. 30 b. 20 c. 40 d. 35

4. If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle?

a. 17m b. 31m c. 12m d. 24m

5. A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

a. 4% b. 300% c. 75% d. 400%

6. A regular hexagon is inscribed in a circle of radius r cms. What is the perimeter of the regular hexagon?

a. 3r b. 6r c. √72r d. 9r

7. If x units are added to the length of the radius of a circle, what is the number of units by

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which the circumference of the circle is increased?

a. x b. 2 c. d.

8. ABCD has area equal to 28. BC is parallel to AD. BA is perpendicular to AD. If BC is 6 and AD is 8, then what is CD?

a. 2√2 b. 2√3 c. 4 d. 2√5

9. Which of the following figures has the largest area?

1. A circle of radius 2. An equilateral triangle whose sides each have length 4 3. A triangle whose sides have lengths 3, 4 and 5

10. The hexagon ABCDEF is regular. That means all its sides are of the same length and all its interior angles are of the same size. Each side of the hexagon is 2 m. What is the area of the rectangle BCEF?

a. 4 sq.m b. 4√3 sq. m c. 8sq.m d. 4+4√3 sq.m

ANSWER KEY

1. A 6. B

2. A 7. D

3. A 8. D

4. D 9. B

5. B 10. D

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CLOCKS, CALENDAR DIRECTIONS and CUBES

Concept 1: Clocks Ex: 1: At what angle the hands of a clock are inclined at 15 minutes past 5?

Solution:

= 30h

m

= (30×5)-(11×15)/2 = 67.5 degree Ex: 2: How many times in a day, are the hands of a clock in straight line but opposite in direction?

Solution: Hands point in the opposite directions 22 times. Ex: 3: A watch gains uniformly is 5 minutes slow at 5:00 a.m. on Wednesday and it is 5 minutes 30 seconds fast at 5:00 a.m. on the following Friday. When was the clock correct?

Solution: On Wednesday on Friday

5 mins slow 5 mins 30 sec fast

48*5 / (10 1/2) = [48/21]*2*5 = 160/7 hours. After 5am on Monday, the clock will show 3.51 am on Thursday

Concept 2: Calendar To find the leap year: For normal values: (year) %4 and for century values: (year) %400 100 years=5 odd days 200 years=3odd days 300years=1 odd days 400 years= 0 odd days

Ex: 1: On what dates of April, 2001 did Wednesday fall? Solution: We shall find the day on 1st April, 2001. 1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001) Odd days in 1600 years = 0 and Odd days in 400 years = 0 Jan, Feb, March, April = (31 + 28 + 31 + 1) = 91 days = 0 odd days. Total number of odd days = (0 + 0 + 0) = 0 on 1st April, 2001 it was Sunday. In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th. Ex: 2: Mrs. Susheela celebrated her wedding anniversary on Tuesday 30th September 1997. When will she celebrate her next wedding anniversary on same day (Tuesday)? Solution: After 7 days=> Days of the week will repeat 30th September - Tuesday 1998 - 1 1999 - 1 2000 - 2 2001 - 1 2002 - 1 2003 - 1

= 30h

m

7 days

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Whatever was the day on 30th sep. 1997, it’ll repeat on 2003!! Therefore, after 1997, next time Mrs.Susheela’s anniversary will be on same Tuesday on 30th September 2003

Concept 3: Cubes and Directions

Three of its faces painted - 8 (corner cubes) Two of its faces painted (edge cubes) - 12(n-2) One face painted (face cube) - 6(n-2)2

No face painted (core cubes) - (n-2)3

Ex: 1: Directions for questions (1-3): A solid cube of side 9 cm has been painted green, red and yellow on pairs of opposite faces. It is then cut into cubical blocks of each side 3 cm.

1. How many cubes have no face painted? Solution: There is only one small cube which is not colored. That is the core cube. No face painted = (n-2)3

N=3, therefore = (3-2)3=1 2. How many cubes have no face painted? Solution: All the corner cubes will be having 3 faces coloured = 8 3. How many cubes have four faces coloured? Solution: There is no small cube with all the four faces colored 4. How many cubes have two face painted? Solution: Two face painted = 12(n-2) = 12(3-2) = 12 PRACTICE QUESTIONS: 1.A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?

n cuts = n+1 pieces

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A. 2 p.m. on Tuesday B. 2 p.m. on Wednesday C. 3 p.m. on Thursday D. 1 p.m. on Friday 2. At what time between 5 and 6 o' clock are the hands of 3 minutes apart? A. 24 B.12 C.13 D.14 3. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25. A. 47.5 degrees B. 57.5 degrees C.45.5 degrees D. 55.5 degrees 4. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004? A. Sunday B. Monday C. Friday D. Saturday 5. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? A. 180 degree B. 45 degree C. 90 degree D. 125 degrees 6. It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010? A. Sunday B. Friday C. Saturday D. Wednesday 7. On what dates of July.2004 did Monday fall? A. 6th, 10th, 21st, 30th B.12th, 7th, 19th, 28th C. 5th, 10th, 24th, 17th D. 5th, 12th, 19th, 26th

8. A cube, painted yellow on all-faces is cut into 125 small cubes of equal size. How many small cubes got no painting? A. 21 B. 8 C. 27 D. 9 9. Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house? A. 10km B. 14km C. 2km D. 16km 10. Sachin walks 20 km towards North. He turns left and walks 40 km. He again turns left and walks 20 km. Finally he moves 20 km after turning to the left. How far is he from his starting position? A.20km B.30km C.10km D.25km Answers:

1 B

2 A

3 A

4 A

5 A

6 B

7 D

8 C

9 A

10 A

Logical Connectives, Syllogisms and Venn Diagrams

Concept 1- Logical Connectives

Sample Statements Conclusion

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If X,Y

Every time X, Y

Whenever X, Y

X=> Y

Y’=> X

Either X or Y

Unless X, Y

X’=> Y

Y’=> X

Only if X, Y X’=> Y’

Y=> X

Ex 1. Whenever I visit my Grandfather, He feels happy.

Conclusion 1: X=> Y; I visited my grandfather so he feels happy.

Conclusion 2: Y’=> X’; My grandfather is not feeling happy since I did not visit him.

Ex 2. He will not be efficient, unless he gets a good night’s rest.

Conclusion 1: X’=> Y; He did not get a good night’s rest so he will not be efficient.

Conclusion 2: Y’=> X; He is efficient since he got a good night’s rest.

Concept 2- Syllogisms

All A are B

X

Some A are B

X X

No A is B

Some A are not B

X

Some + Some => No Conclusion No+ No=> No Conclusion

All+ Some => Some All+ No => No

Ex 1. Find out the conclusion for the following statements

I. All lights are bright

II. Some bright are reflections

All + Some => Some

Some lights are reflections

Ex 2. Statements:

I. All Vehicles are cars

II. Some cars are cycles

III. All cycles are tires

Conclusions:

I. Some tires are Vehicles

II. Some cars are Vehicles

II. Some tires are cars

II is the only connecting statement

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Conclusion cannot be derived by combining I and II

Combining II and III, we get some tires are cars

Hence only conclusion III follows

Concept 3- Venn Diagrams

1. 200 students appeared for two different examinations. 120 passed the first, 100 the

second and 60 both examinations. Find the probability that a student selected at random

failed in both examinations?

o A + B + C + U = 200

o C = 60

o A = 120 - 60 = 60

o B = 100 - 60 = 40

o U = 200 - 160 = 40

o P(U) = 40/200 = 1/5

2. Out of 400 people who went to a function, 240 coffee, 200 drank tea, 160 drank fruit juice

and 10 had none of these three. 200 people had exactly one of the three items. How many

people had exactly two of the three items?

Since 10 had none, 390 had at least one item

g + a + e + b + d + f + c = 390 ________(1)

g + a + e + 2b + 2d + 2f + 3c = 600_____(2)

Substituting (1) in (2),

b + d + f + 2c = 210_________________(3)

g + a + e = 200_____________________(4)

2b + 2d + 2f + 3c = 400_______________(5)

Substituting (3) in (5),

c = 20

From (3)

b + d + f = 170

Practice Exercise

1. A College has three clubs. Only three persons are members of all three clubs, but every pair

of clubs has four members in common. What is the LEAST possible number of members on

any one club?

b. 3 b. 4 c. 5 d. 6

2. Out of 300 people who attended a party, 180 were dancing, 150 were drinking, 120 were

singing and 15 did not do any of them. 150 people did exactly one of the three things. How

many people did exactly two of the three things?

a. 150 b. 140 c. 165 d. 105

c

Coffee

Tea Juice

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3. Each of the following questions has a main statement followed by four statements. Choose

the pair from the given options where the third statement can be logically concluded from

the previous two, including the main statement.

All papers are scissors

A. Some lizard are papers

B. Some lizard are Spock

C. Some Spock are papers

D. Some lizards are scissors

a. AD b. DA c. CB d. AC

4. Statements: All ash are sri. All sri are dale.

Conclusions: I. All ash are dale. II. All dale are ash.

a. I b. II c. Both I&II d. None

5. Each question has two statements and some conclusion. Choose the conclusion that

logically follows: Whenever Ashwin entered the class, the girls booed.

A. Ashwin entered

B. The girls didn’t boo

C. Ashwin didn’t enter

D. The girls booed

a. BC b. AD c. DA d. CB

6. I laugh out loud every time I hear a joke

A. I laughed out loud

B. I didn’t laugh out loud

C. I heard a joke

D. I didn’t hear a joke

a. CA b. BD c. AC d. DB

7. Each of these questions consists of six statements followed by four sets of three statements

each. Select as your answer the set in which the statements are logically related (in any

order)

(1) All love are stupid.

(2) All stupid are difficult.

(3) No difficult is dangerous.

(4) Some love are not important.

(5) Some difficult are not love.

(6) All love are difficult.

a. 452 b. 156 c. 216 d. 341

8. Either I will go out or I will sleep.

A. I went out

B. I didn’t go out

C. I slept

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D. I didn’t sleep

What may be the conclusion?

a. BC b. CB c. AD d. None

9. 200 students went to Blooper’s stop. 120 purchased rug, 100 purchased drag and 60 both.

Find the probability that a student selected at random is a window shopper?

a. 1/6 b. 1/5 c. 3/5 d. 1/3

10. Each of the following questions consists of six premises followed by five options consisting

of three statements put together in a specific order. Choose the option which indicates a

valid argument that is when the third statement is a conclusion drawn from the preceding

two premises.

i. All readers are ping pong players

ii. Some readers are not chess players.

iii. No intelligent is happy

iv. Some readers are not wise.

v. All happy are wise.

vi. No ping pong player is chess player.

b. CED b. ABF c. AFB d. ACD

Key:

1 C 6 D

2 D 7 C

3 A 8 A

4 A 9 B

5 B 10 B

Data Interpretation

Concept 1: Bar-Chart

Directions for Question 1 to 3: Refer to the following Bar-chart and answer the questions that

follow

1: What is the average value of the contract secured during the years shown in the diagram? (a) Rs. 103.48 crore (b) Rs. 105 crore (c) Rs. 100 crore (d) Rs.125.2 crore Solution: (100.5 + 67 + 141 + 143.9 + 65)/5 = 103.48 crore.

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2. Compared to the performance in 1985 (i.e. taking it as the base), what can you say about the performances in the years ’84, ’85, ’86, ’87, ’88 respectively, in percentage terms?

(a) 150, 100, 211, 216, 97 (b) 100, 67, 141, 144, 65 (c) 150, 100, 200, 215, 100 (d) 120, 100, 220, 230, 68 Solution: The performance of only year i.e. 88 is less than the year 85. Hence the percentage corresponding to 1988 should be less than 100. Thus (c) cannot be the answer. Also (b) cannot be the answer as it shows two of the years having less than 100%. Between options (a) and (d), the correct answer is (a). Since the difference between the 1985 and 1988 performance is only 2 units on 67 units. Hence percentage-wise, it has to be 97% and not 68%. 3. Which is the year in which the highest percentage decline is seen in the value of contract secured compared to the preceding year? (a) 1985 (b) 1988 (c) 1984 (d) 1986 Solution: The highest percentage decrease over the previous year is in year 1988, and the performance is almost half than that of the previous year. Such a decrease is not seen in any other year, so the right answer is Option b

Concept 2: Pie Charts

Direction for questions 4 to 5: Answer the questions based on the following pie charts.

1. The operating profit in 1991-92 increased over that in 1990-91 by a. 23% b. 22% c. 25% d. 24% Solution: Percentage increase = (160 – 130)100/130 = 300/13 = 23% Option a 2. The interest burden in 1991-92 was higher than that in 1990-91 by a. 50% b. Rs. 25 lakh c. 90% d. Rs. 41 lakh Solution: Interest in 1990-91 = 30% of 130 = Rs. 39 lakh Interest in 1991-92 = 40% of 160 = Rs. 64 lakh Hence, difference = (64 – 39) = Rs. 25 lakh Option b

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Concept 3: Data Sufficiency:

Two types of questions: Data sufficiency questions are of two types.

Type 1 Questions: These questions start with "with what, who, how,... etc". Type 2 Questions: These questions start with a helping verb like "is, does, are, etc".

So answers for these questions are yes, no, or data insufficient Using the data given in the statements, indicate whether - Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. EACH statement ALONE is sufficient to answer the question asked. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. Example 1: Is Raja older than Ramu? I. Sita is 4 years younger than Raja and 2 years younger than Ramu. II. The average age Raja and Ramu is 21 years. Solution: This is a type 2 question. Let Sita’s age be 20. Then Raja’s age is 24, and Ramu’s age is 22. So clearly Raja is older than Ramu. So Statement I is sufficient to answer this question. Statement II, however, gives only the average age but nothing about their individual ages. The correct answer choice is Option a . Example 2: What is the value of x? I. x2 = 16 II. x > 0 Solution: From statement I we can see that x = +4 or x = –4. Now we may be tempted to consider this as a valid answer, as we have determined the value of x. But since this is not a unique answer, such an answer is not valid. So statement I alone is not sufficient to answer the question. Statement II alone does not give a definite answer as there are infinite numbers greater than 0. By combining both the statements we can conclude that x takes +4. So correct answer is Option c.

Practice questions: Answer the questions based on the following table.

The table gives the production of major agricultural products in Million Tonnes (MT).

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1. The agro product which witnessed the highest growth rate in production from 1997 to

2000 is

a. Wheat b. Rice c. Sugar Cane d. Pulses

2. Pulses production in 1998 is what percent of the total production of rice in the given 4-

year period?

a. 19.13 b. 19.58 c. 20.38 d. 19.38

3. By what percent is the average wheat production more than the average sugar cane

production for the given 4-year period?

a. 535 b. 529 c. 629 d. 502 (Q4 – Q6) These questions are based on following graphs Classification of appeared candidates in a competitive test from different states and qualified candidates from those states.

4. What is the ratio between the number of appeared candidates from states C and E together and the appeared candidates from states A and F together? a. 17: 33 b. 11: 13 c. 13: 27 d. 17: 27 5. In which State the percentage of qualified candidates to that of appeared candidates minimum? a. C b. F c. D d. E 6. What is the difference between the number of qualified candidates of states D and G a. 690 b. 670 c. 780 d. 720 7. What is the volume of a right circular cylinder? I. The area of the base of the figure is 196. II. The height of the figure is 16 8. How old is Subhash? I. In 16 more years Subhash will be twice as old as he is today. II. Four years ago Subhash was 3/4 times of his present age. 9. If x, y and z are consecutive integers, is y even? I. x < y < z

http://1.bp.blogspot.com/-6p5GSknLU8o/Ux1IIGweMLI/AAAAAAAAIQ4/tfHjf9hxAAc/s1600/4.png

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II. xz is odd integer 10. How many students are enrolled in Sastri's Quant class? I. If 3 more students sign up for the class and no one drops out, more than 35 students will have enrolled in the class. II. If 4 students drop out of the class and no more sign-up, fewer than 30 students will have enrolled in the class.

Answer Key

DATA ARRANGEMENTS

LINEAR ARRANGEMENT

A. There are five friends.

B. They are standing in a row facing south.

C. Jayesh is to the immediate right to Alok.

D. Pramod is between Bhagat and Subodh.

E. Subodh is between Jayesh and Pramod.

1. Who is at the extreme left end?

2. Who is in the Middle?

SOLUTION:

A J S P B

CIRCULAR ARRANGEMENT

6 people A to F are sitting in a round table. A is not adjacent to B or C; D is not adjacent to C

or E; B and C are adjacent; F is in the middle of D and C.

1. If one neighbour of A is D, who is the other one? 2. Who is sitting opposite to C? SOLUTION:

1. C 6. D

2. D 7. C

3. D 8. E

4. A 9. A

5. D 10. C

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BLOOD RELATIONS

1. Pointing towards a person in a photograph, Anjali said, "He is the only son of the

father of my sister's brother." How that person is related to Anjali?

Ans: Brother

PRACTICE EXERCISE:

1. If Kamal says, "Ravi's mother is the only daughter of my mother", how is Kamal

related to Ravi?

a. Brother b. Father c. Maternal uncle d. Cousin

2. Pointing to a photograph, a woman says, "This man's son's sister is my mother-in-

law." How is the woman's husband related to the man in the photograph?

a. Grandson b. Son c. Son-in-law d. Cousin

3. If Neena says, "Anita's father Raman is the only son of my father-in-law Mahipal",

then how is Bindu, who is the sister of Anita, related to Mahipal?

a. Granddaughter b. Daughter c. Sister d. None

Direction for questions from 4-7:

In a class there are seven students (including boys and girls) A, B, C, D, E, F and G.

They sit on three benches I, II and III. Such that at least two students on each bench

and at least one girl on each bench. C who is a girl student, does not sit with A, E and

D. F the boy student sits with only B. A sits on the bench I with his best friends. G sits

on the bench III. E is the brother of C.

4. How many girls are there out of these 7 students? a. 3 b. 3 or 4 c. 5 d. Data inadequate

5. Which of the following is the group of girls?

a. BAC b. BFC c. BCD d. CDF

6. Who sits with C?

a. B b. D c. G d. E

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7. On which bench there are three students?

a. Bench I b. Bench II c. Bench III d. Bench I or II

Direction for questions from 8 to 10

Akshay, Manisha, Deepak, Paresh, Ranbir, Tarun, Bector and Hrithik are sitting around a circle facing at the centre. Manisha is 3rd to the left of Akshay who is 2nd to the left of Tarun. Deepak is 2nd to the right of Hrithik who is 2nd to the right of Tarun. Ranbir is 2nd to the right of Bector who is not an immediate neighbour of Tarun.

8. Which of the following combinations represents the first and the second to the left of Bector respectively?

a. Manisha and Deepak b. Deepak and Hrithik

c. Akshay and Manisha d. Deepak and Manisha

9. Who is 3rd to the right of Tarun?

a. Paresh b. Manisha c. Tarun d. Ranbir

10. Who is 2nd to the left of Bector?

a. Deepak b. Hrithik c. Manisha d. Inadequate

ANSWER KEY:

1(c) 2(a) 3(a) 4(b) 5(c)

6(c) 7(a) 8(d) 9(b) 10(c)

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SENTENCE CORRECTION

SUBJECT VERB AGREEMENT

(i) Words like everyone, everybody, everything, somebody, something, someone, nobody,

nothing, no one etc takes the singular verb. Example, ”Everybody knows French here.”

(ii) Non Intervention Principle.

When the subject in the sentence is followed by some prepositional phrases like; along

with, together with, in addition to, as well as, except etc., the verb form is determined by

the main subject. Example, “Ram along with his brothers is going to the theatre.”

(iii)Proximity rule

When you use "neither....nor" and "either....or", the number of subjects closer to the verb

determines if you have to use a singular or a plural form of verb.

Example: Neither her friends nor she is interested in joining the club.

MODIFIER

Modifiers are words or phrases that will modify the words or a phrase. A misplaced modifier

occurs when you put a modifying word or phrase in the wrong place in a sentence.

To correct it, move the offending word or phrase to the right place in the sentence, make

sure that the modifier and the thing it’s modifying are as close together as possible in the

sentence, and try not to let anything between the modifier and the thing it’s modifying.

Example: “The cops chased the bear in the squad car.”

This sentence tells us that the bear is in the squad car, not the cops. To fix this mistake, let’s

move our modifying phrase, “in the squad car,” closer to the cops. So, the corrected

sentence will be “The cops in the squad car chased the bear.”

PRONOUN-ANTECEDENT AGREEMENT ERROR.

A pronoun agrees with its antecedent in number, gender, and person.

(i) If the antecedent is singular, a singular pronoun is required. The plural antecedent

requires a plural pronoun. For example, “Each of the boys has his own savings account”.

(ii) Singular antecedents joined by or/nor are referred to by a singular pronoun. For

example, “John nor Dave could find his jacket”.

(iii) Collective nouns may take either a singular or plural pronoun, depending on the

meaning of the sentence. For example, ”The cast is having its picture taken”. (whole group

as one)

VERB TIME SEQUENCE ERROR

Verb tenses exist in order to allow us to specify at what point in time some event occurred.

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EG1: Incorrect: After he had finished his performance, he would go to the party.

Correct: After he had finished his performance, he went to the party.

Both events - the performance and the party - happened in the past, but the performance

happened first, and the party second. Thus both verbs should be in the past tense: had

finished in past perfect, to indicate that the performance happened first, and then went in

simple past.

DETERMINERS:

Quantifiers that can be used with countable nouns are: many, few, a few, several, a couple of, none The following quantifiers are used with non-countable nouns: much, little, a bit of. Some quantifiers that is used as both countable and uncountable nouns are: some, all, most, enough, a lot of, lots of, plenty of, a lack of. There is an important difference between a little and little and between a few and few. EG1: Merlin has a little experience in graphics designing. (= Merlin is no expert graphics designer; however, she does have some experience in graphics designing and that should be enough for our purposes. EG2: Merlin has little experience in graphics designing. (= Merlin doesn’t have enough experience. We had better find somebody else.) EG3: My sister has written a few books on child psychology. (= She has written some books – not a lot of books) EG4: I have read few books on Indian mythology. (= I haven’t read enough books on Indian mythology.)

SENTENCE COMPLETION

Different strategies that can be used for solving sentence completion questions are as follows, PROACTIVE SOLVING: The first thing that you should do while solving sentence completion

questions is, read the question and try to guess the meaning of the word that should be.

For example, when you have a question like this:-

“The politician’s comment about the community was so ______ that even his own party

members rebuked him for it”.

From this, you know that, the comment given by the politician was something negative

(a) Honest. (b) Objectionable. (c) Incompetent. (d) Objective.

Options (a) and (d) are obviously eliminated because; they do not fit the proper meaning

that the sentence is trying to convey. Incompetent means ‘lacking necessary ability’.

Comment cannot be associated with lacking necessary ability. So, the answer is definitely

Option (b) Objectionable.

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SIGNPOST CLUES:

Hamsters are _____ and gentle creatures who will fill your world with more love and joy

than you could ever anticipate.

(a) Vicious (b) Determined (c) Docile (d) Uncultivated

Here, there is a signpost word ‘and’. This means the word in the blank should be related to

gentle. Thus, we can eliminate options (a), (b) and (c). Yes, without even knowing the

meaning of ‘docile’, we can be sure that the answer is option (b) docile

Monica is quite intelligent but rather _____.

(a) Idealistic (b) Generous (c) Lazy (d) Optimistic

There is a signpost word ‘but’ in the question. Intelligent is a positive comment. So, the

answer must be a negative comment. So, the answer cannot be options (a), (b) or (d). So,

the answer is option (c) Lazy.

ROOTWORD CLUES

A person unrestrained by rules of morality or tradition is called a _____.

(a) Libertine (b) Criminal (c) Freelancer (d) Convict

The word in the blank should mean that the person is free. Freelancer is person who works

for various companies independently. So, it is not option (c). The root word ‘liberty’ means

freedom. So, it definitely has to be option (a) Libertine.

PARA JUMBLES

In a Para-jumble question you don’t have to read and understand all the statements to

construct a meaningful passage. It can be done using a few clues and reactive solving (From

the options). In a Para-jumble question first thing to be done is to identify the first and last

sentence, and also identify the compulsory pairs (Noun-Pronoun pair).

S1: The cooperative system of doing business is a good way of encouraging ordinary workers

to work hard.

P: If the society is to be well run, it is necessary to prevent insincere officials being elected to

the committee which is solely responsible for the running of the business.

Q: They get this from experienced and professional workers who are not only familiar with

the cooperative system, but also with efficient methods of doing business.

R: To a large extent, many cooperative societies need advice and guidance.

S: The capital necessary to start a business venture is obtained by the workers'

contributions.

S6: The main objective is to maintain the interest of every member of the society and to

ensure that the members participate actively in the projects of the society.

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(a) SQPR (b) PQSR (c) SRQP (d) PSRQ

Now, by glancing through all the statements, we can get a general idea on how to solve it.

Now, statement Q has “They get this”. What does ‘this’ refer to? It says they get it from

experienced and professional workers who know efficient methods of doing work. Now, if

we go through the statements, we can see that, it is statement R, which says many

cooperative societies need advice and guidance. This is what the ‘this’ in statement Q refers

to. So, RQ is a compulsory pair. Any option which does not have RQ together can be

eliminated. So, option (a) and (b) can be eliminated.

Now, let us apply the seek general to specific transitions rule. So, the first statement should

be statement S (Because it talks about the starting of the business venture). Hence, the

correct answer is option (c).

VOCABULARY

The different strategies to solve the questions from antonyms, synonyms and analogies are

as mentioned below.

PREFIXES AND SUFFIXES

Prefixes are added before a root word and suffixes are added after a word.

Examples for prefixes: pre, un, dis, mal, mis, co

Examples for suffixes: ful, ment, less, able, ed, ness .

Depending on the prefix used the meaning of the word varies with respect to the root word.

The suffix helps us ascertain which part of speech the word belongs to.

1) Malodorous: “mal” is the prefix used. We know many words having the prefix mal:

malpractice, malnutrition etc. All these words contain a common meaning- bad.

Odorous is the root word with meaning “something related to smell”

2) The words ending with “age will be a noun. Egs: adage, salvage storage.

3) The words ending with “able” will be an adjective. Egs: amiable, agreeable, and

capable.

USING CONTEXTUAL MEANING

Sometimes what actually goes wrong is the meaning of the word in that particular context,

sometimes it is not the definitive meaning of the word but it is metaphorical meaning. So

you need to be very clear with the sentence understanding to answer it correctly. Reading in

context helps you the most of the time to solve the word meanings given in a sentence.

The rescue crew was undaunted by the flames and ran into the burning house look for

survivors.

a)fearless b)discouraged c)demoralised d)frightened

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From the context, we can predict the meaning of the word undaunted by proactive solving.

They ran into the burning house-shows they are fearless.

STATEGIES TO SOLVE ANALOGIES:

We have to find the relationship between words and find similar relationship in the answer

options.

1. The relationships can be synonyms. Ex: wealthy: affluent: : indigent : poverty-stricken

2. Oppositeness (antonyms). Ex: zenith: nadir: : pinnacle : valley

3. Classification Order (general - specific). Ex: orange: fruit: : beet : vegetable

4. Difference of Degree (or Connotative Values). Ex: clever: crafty : : modest : prim

5. Person Related to Tool, Trait, Skill, or Interest. Ex: entomologist: insects : : philosopher :

ideas

6. Part and Whole. Ex: eraser: pencil : : tooth : comb

7. Steps in a Process. Ex: cooking: serving: : word processing : printing

8. Cause and Effect (or Typical Result). Ex: fire : scorch : : blizzard : freeze

9. Thing and Its Function. Ex: scissors: cut: : pen : write

10. Qualities or Characteristics. Ex: aluminium: lightweight: : thread : fragile

11. Implied Relationships. Ex: clouds: sun : : hypocrisy : truth

PRACTICE EXCERCISE

1. As a result of consumers' increased awareness of the health risks associated with heavy consumption of red meat, the meat of the ostrich has become increasingly popular as a low-fat, low-cholesterol alternative to beef. Accordingly, the number of ostrich farms in the United States has nearly quadrupled since 1980, flooding markets with ostrich products. However, the price-per-pound of ostrich meat, adjusted for inflation, has not decreased at all over the past several years. Which of the following, if true, would best explain the steady price-per-pound of ostrich meat?

A. The demand for ostrich products has outpaced the supply. B. Ostriches are especially difficult to breed in captivity. C. Other types of meat, such as pork and poultry, have decreased in price over the past

several years. D. Purveyors of beef have not attempted to counter beef's poor public image. E. The number of supermarkets that carry ostrich meat has increased steadily since

1980.

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2. According to a recent magazine article, of those office employees who typically work 8 hours at the office each day but sometimes say that they will work at home on a particular day, 25 percent actually work less than one hour. At the same time, over 90 percent of those same office employees believe they are more productive working at home than working in their office. The statements above, if true, best support which of the following conclusions about the office employees discussed in the article?

A. On average, the office employees working at home for a day work fewer hours than office employees working at the office.

B. 10 percent of the office employees are less productive working from home than working in their office.

C. At least 15 percent of the office employees do not define productivity exclusively in terms of the number of hours worked.

D. At least 25 percent of the office employees can complete the same amount of work in one hour at home as in 8 hours at the office.

E. Some of the office employees make statements regarding their productivity that are not in fact true.

QUESTIONS:[3-6]

The name of Florence Nightingale lives in the memory of the world by virtue of the heroic adventure of the Crimea. Had she died - as she nearly did - upon her return to England, her reputation would hardly have been different; her legend would have come down to us almost as we know it today - that gentle vision of female virtue which first took shape before the adoring eyes of the sick soldiers at Scutari. Yet, as a matter of fact, she lived for more than half a century after the Crimean War; and during the greater part of that long period all the energy and all the devotion of her extraordinary nature were working at their highest pitch. What she accomplished in those years of unknown labour could, indeed, hardly have been more glorious than her Crimean triumphs; but it was certainly more important. The true history was far stranger even than the myth. In Miss Nightingale's own eyes the adventure of the Crimea was a mere incident scarcely more than a useful stepping-stone in her career. It was the fulcrum with which she hoped to move the world; but it was only the fulcrum. For more than a generation she was to sit in secret, working her lever: and her real life began at the very moment when, in popular imagination, it had ended. She arrived in England in a shattered state of health. The hardships and the ceaseless efforts of the last two years had undermined her nervous system; her heart was affected; she suffered constantly from fainting-fits and terrible attacks of utter physical prostration. The doctors declared that one thing alone would save her - a complete and prolonged rest. But that was also the one thing with which she would have nothing to do. She had never been in the habit of resting; why should she begin now? Now, when her opportunity had come at last; now, when the iron was hot, and it was time to strike? No; she had work to do; and,what might, she would do it. The doctors protested in vain; in vain her family lamented and entreated, in vain her friends pointed out to her the madness of such a course. Madness? Mad -possessed - perhaps she was. A frenzy had seized upon her. As she lay upon her sofa,

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gasping, she devoured blue-books, dictated letters, and, in the intervals of her palpitations, cracked jokes. For months at a stretch she never left her bed. But she would not rest. At this rate, the doctors assured her, even if she did not die, she would become an invalid for life. She could not help that; there was work to be done; and, as for rest, very likely she might rest ... when she had done it. Wherever she went, to London or in the country, in the hills of Derbyshire, or among the rhododendrons at Embley, she was haunted by a ghost. It was the spectre of Scutari - the hideous vision of the organization of a military hospital. She would lay that phantom, or she would perish. The whole system of the Army Medical Department, the education of the Medical Officer, the regulations of hospital procedure ... rest? How could she rest while these things were as they were, while, if the like necessity were to arise again, the like results would follow? And, even i peace and at home, what was the sanitary condition of the Army? The mortality in the barracks, was, she found, nearly double the mortality in civil life. 'You might as well take 1, 100 men every year out upon Salisbury Plain and shoot them,' she said. After inspecting the hospitals at Chatham, she smiled grimly. 'Yes, this \is one more symptom of the system which, in the Crimea, put to death 16,000 men.' Scutari had given her knowledge; and it had given her power too: her enormous reputation was at her back - an incalculable force. Other work, other duties, might lie before her; but the most urgent, the most obvious, of all was to look to the health of the Army.

3. According to the author, the work done during the last fifty years of Florence Nightingale's life was, when compared with her work in the Crimea, all of the following except,

A. less dramatic B. less demanding C. less well-known to the public D. more important

4. The 'fulcrum' (line 17) refers to her

A. reputation B. mental energy C. physical energy D. overseas contacts E. commitment to a cause

5. Paragraph two paints a picture of a woman who is an incapacitated invalid

A. mentally shattered B. stubborn and querulous C. physically weak but mentally indomitable

6. The primary purpose of paragraph 3 is to,

A. account for conditions in the army B. show the need for hospital reform

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C. explain Miss Nightingale's main concerns D. argue that peacetime conditions were worse than wartime conditions

7. Birds are _______ to prevent the spread of bird flu.

A. Immunized

B. Butchered

C. Secluded

D. Mingled

8 . People often revel under the assumption that only the poor and less educated people

use slang but this idea is so _____.

A. Accurate

B. Popular

C. Erroneous

D. Ineffective

9. I was feeling rather _____ when I _____ a yellow envelope on the table.

A. happy, discerned

B. jubilant, glimpsed

C. ecstatic, perceived

D. miserable, spotted

10. We have in America a _____ speech that is neither American, Oxford English, nor

colloquial English, but a _____ of all three.

A. Motley, an enhancement

B. Hybrid, a combination

C. Nasal, A blend

D. Mangled, a medley

11. Corruption is ____ in our society; the integrity of even senior officials is____

A. growing – unquestioned

B. endangered – disputed

C. pervasive – intact

D. rifle – suspected

12. Arrange the sentences in proper order.

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S1: American private lives may seem shallow.

P: Students would walk away with books they had not paid for.

Q: A Chinese journalist commented on a curious institution: the library.

R: Their public morality, however, impressed visitors.

S: But in general they returned them.

S6: This would not happen in China, he said.

A. PSQR

B. QPSR

C. RQPS

D. RPSQ

13. Haggard (synonym)

A. Healthy

B. weakened

C. strong

D. colourful

14. Malicious (Synonym)

A. venomous

B. forgiving

C. benevolent

D. useful.

15. Determined (Antonym)

A. Damaging

B. Injurious

C. Beneficial.

D. Destructive.

16. Prodigality

A. Extravagancy

B. lack

C. wastefulness

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D. overdoing.

17. Ornithologist: Birds:: Archaeologies: ___________

A. islands

B. mediators

C. aquatic

D. artefacts

18. Eye : Myopia :: teeth : _________

A. Pyorrhoea

B. Cataract

C. Trachoma

D. Eczema

19. Denim jeans were originally worn not so much as a fashion statement as for their being practical work clothes.

A. Denim jeans were originally worn not so much as a fashion statement as for their being

practical work clothes.

B. Denim jeans were originally worn not so much as a fashion statement but for their being

practical work clothes

C. Denim jeans were originally worn not so much as a fashion statement but for being

practical work clothes

D. Denim jeans were originally worn not as a fashion statement as for them being practical

work clothes.

20. None of the presents I received (A) on my birthday this year was (B) equally (C) as

memorable as the necklace you gave (D) me last year. No error (E).

ANSWER KEYS:

1-A 2-C 3-B 4-A 5-D

6-C 7-C 8-C 9-D 10-B

11-D 12- B 13-B 14-A 15-C

16-B 17-D 18-A 19-A 20-C

aptitude

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