quantitative ability - level c

NARENSINSTITUTE FOR COMPETITIVE EXAMINATIONSQUANTITATIVE ABILITY LEVEL - C

Numerical ReasoningProblems on NumbersProblems on AgesRatio and ProportionAlligation or MixtureChain RulePartnershipVenn Diagram

Numerical ReasoningArea and VolumeProbabilityTime and Work (Pipes)SI and CIAveragePermutation and CombinationPercentageCubes

Numerical ReasoningBoats and StreamsTime and Distance (Trains)Data SufficiencyProfit and LossCalendarClocksData Interpretation

Problems on NumbersArithmetic Progression: The nth term of A.P. is given by Tn = a + (n 1)d; Sum of n terms of A.P Sn = n/2 *(a + L) or n/2 *[2a+(n-1)d)]

a = 1st term, n = number of term, d= difference, Tn = nth term

Geometrical Progression: Tn = arn 1.

Sn = a(rn 1)/(r-1); a = 1st term , r = 1st term / 2nd term

Basic Formulae1. ( a+b)2 = a2 + b2 + 2ab2. (a-b)2 = a2 +b2 -2ab3. ( a+b)2 - (a b)2 = 4ab4. (a+b)2 + (a b)2 = 2 (a2 +b2)5. (a2 b2) = (a+b) (a-b)6. (a+b+c)2 =a2 +b2 +c2 + 2(ab +bc+ca)7. (a3 +b3) = ( a+b) (a2 ab +b2)8. (a3 b3) = (a-b) (a2 +ab + b2)9. (a3+b3+c3 -3abc) = (a+b+c) (a2+b2+c2-ab-bc-ca) If a+b+c = 0, then (a3+b3+c3) =3abc

Problems on Numbers A man ate 100 Bananas in 5 days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?

Problems on NumbersSolution:First day be xThen x+6, x+12, x+18, x+245x + 60 = 100 x=8In first day he ate 8 Bananas.

Problems on NumbersThe traffic light at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds respectively. If they all change simultaneously at 10:20:00 hours then at what time they again change simultaneously?

Problems on NumbersSolution:

LCM (48,72,108) = 432 seconds = 7 minutes 12 secondsThe next change will be at 10:27:12 hours

Problems on NumbersRaja had 85 currency notes in all, some of which were of Rs. 100 denomination and the remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount did she have in the denomination of Rs. 50?

Problems on NumbersSolution: Let x be the number of Rs. 50 notes50x + 100 (85-x) = 5000Solving the above equation,Amount = Rs. 3500

Problems on NumbersMr. Raja is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. For how many days is Mr. Raja on tour?

Problems on NumbersSolution: Let x be the number of days

360 / x 360 / (x+4) = 3

Solving the above equation,

The number of days of the tour x = 20 days

Problems on NumbersIf the numerator of a fraction is increased by 25% and the denominator is decreased by 20% the new value is 5/4. What is the original value?

Problems on NumbersSolution:NR = x + 25x/100DR = y -20y/100(5x/4)/(4y/5) =5/4Solving the equation,The fraction is 4/5

Problem on NumbersThere is a circular pizza with negligible thickness that is cut into X pieces by 4 straight line cuts. What is the maximum and minimum value of x respectively?

Problem on NumbersAnswer:Maximum = 11.Minimum = 5.

Problem on NumbersA man was engaged on a job for 30 days on condition that he would get a wage of Rs. 10 for the day he works but he has to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end. Find the number of days he was absent?

Problem on NumbersSolution:10x 2(30 x) = 216x = 23Absent for = (30 23) = 7 days

Problems on Numbers

I bought a car with a peculiar 5-digit number license plate which on reversing could still be read. On reversing the value is increased by 78633. What is the original number if all the digits were different from 0 - 9?

Problems on NumbersSolution:

Only 0,1,6,8,9 can be reversed. Hence the number is 89601. Its reverse is 10968 and difference is 78633

Problems on NumbersNaval collected 8, spiders and beetles in a little box. When he counted the legs he found that they were altogether 54. How many beetles and how many spiders did he collect?

Problems on NumbersSolution:Spiders have 8 legs and beetles have 6 legs.S + B = 8,8S + 6B = 54.Solving the above equationsThe number of spiders = S = 3The number of beetles = B = 5

Problems on AgesFathers age is three times the sum of the ages of his two children, but twenty years hence his age will be equal to sum of their ages ?

Problems on AgesSolution:

Father age = 3(x+y)F+20 = x+y+403x+3y+20 = x+y+403x-x+3y y =202x+2y = 20 x +y = 10F = 3*10 =30 The fathers age is 30.

Problems on AgesA mans age is 125% of what it was 10 years ago, but 83 1/3% of what it will be after ten years. What is his present age?

Problems on AgesSolution:Let the present age be x years,Then, 125% of (x-10) = x83 1/3% of (x+10) = x125% of (x-10) = 83 1/3 % of (x+10)5/4 (x-10) = 5/6 (x+10)5x/12 = 250 / 12 x = 50 years

Problem on AgesMy age three years hence multiplied by 3 and from that subtracted three times my age three years ago will give you my exact age. Find my age?

Problem on AgesSolution:(x+3)3 3(x-3) = xx =18

Problem on AgesA boy asks his father What is the age of grand father? Father replied He is x years old in x2 years and also said We are talking about 20th century What is the year of birth of grand father?

Problem on AgesSolution:20th century means 1900 2000 year Perfect square 44 * 44 = 1936 (present)Year of birth = 1936 - 44 = 1892

Problem on AgesA wizard named Nepo says I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old. How old is Nepo?

Problem on AgesSolution:N = 3SF = 40 + 2NF + N + S = 1240Solve 3 equationsAge of Nepo = 360 years

Problems on AgesJoes father will be twice his age 6 years from now. His mother was twice his age 2 years before. If Joe will be 24 two years from now, what is the difference between his fathers & mothers age? (TCS)

Problems on AgesSolution:F + 6 = 2(J +6)M-2 = 2(J-2)Joe is now 22, F = 2(22) +12 6 = 50M = 2(22) 4+2 = 42Difference = 50 -42 =8

Problems on AgesOne year ago the ratio of Baskarans and Saraswatis age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Saraswathi?

Problems on AgesSolution:One year ago,Baskarans age = 6xSaraswathis age = 7xFour years hence[(6x + 1) + 4] / [(7x+1) + 4] = 7 / 8Simplifyingx =5Saraswathis present age is 7x +1 = 36 years

Puzzle

Can you make 120 by using 5 zeros?

PuzzleSolution:Fact (0! + 0! + 0! + 0! + 0!) = Fact (5) = 5! = 120

Ratio and Proportion Ratio: The Relationship between two variables is ratio.

Proportion: The relationship between two ratios is proportion.

Ratio and Proportion The two ratios are a : b and the sum nos. is x ax bx -------- and ------- a + b a + b

Similarly for 3 numbers a : b : c

Ratio and ProportionA sporting goods store ordered an equal number of white and yellow balls. The tennis ball company delivered 45 extra white balls making the ratio of white balls to yellow balls 1/5 : 1/6. How many white tennis balls did the store originally order for? (TCS Question)

Ratio and ProportionSolution: Let the number of yellow balls be x

(x + 45) : x = 1/5 : 1/6


The number of white balls originally ordered

would be = 225 balls

Ratio and ProportionThe ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameters 2 cm and 4 cm respectively?

Ratio and ProportionSolution:R1 = 1st PipeR2 = 2nd PipeR1 1/r12R2 1/r22R1: R2 = 1/r12: 1/r22 = 1/12: 1/22 = 1/1: 1 / 4 = 4:1Ratio of rates of flow is 4:1

Ratio and Proportion

I participated in a race. 1/5th of the participants were before me and 5/6th of them behind me. Find the total number of participants.(Infosys Question)


Solution:

Let the total number of participants be x.

(x 1)/5 + 5 (x-1)/6 = x


The total number of participants would be = 31


If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, find A : D?

Ratio and Proportion Solution :

(A /B *B/C*C/D) =2/3*4/5*6/7

A : D = 16 : 35

Ratio and ProportionA bag contains 50 paise, 25 paise and 10 paise coins in the ratio 5 : 9 : 4, amounting to Rs. 206.Find the number of coins of each type.

Ratio and ProportionSolution : The actual ratio would be5 * 50/100 : 9 * 25/100 : 4 * 10/100 = 50 : 45 : 8Value of 50 paise coins=206*50/103=10025paise coins =206*45/103=9010paise coins =206*8/103 =16Deriving from this ratio,Number of 50 paise coins = 100*2=200Number of 25 paise coins = 90*4 =360Number of 10 paise coins = 16*10 =160

Ratio and ProportionThere are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole. How much time will it take to reach the last pole?

Ratio and ProportionSolution:11 : 19 = 24 : x

By Solvingx = 41.45 seconds

Ratio and ProportionAnnual incomes of A and B is in the ratio 5 : 4 and their annual expenses bear a ratio of 4 : 3. If each of them saves Rs. 500 at the end of the year then find the annual income.

Ratio and ProportionSolution:IncomeA : B = 5x : 4xExpenses A : B = 4y : 3y5x 4y = 500 and 4x 3y = 500Solving the above equations,As annual income = Rs. 2500Bs annual income = Rs. 3500

PuzzleCan you draw three concentric circles with a line passing through their center without lifting hand?

Alligation or Mixture(Quantity of cheaper / Quantity of costlier) (C.P. of costlier) (Mean price)= -------------------------------------- (Mean price) (C.P. of cheaper)

Alligation or Mixture

Cost of Cheaper Cost of costlier c d

Cost of Mixture m

d-m m-c

(Cheaper quantity) : (Costlier quantity) = (d m) : (m c)


A merchant has 100 kg of salt, part of which he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole. Find the quantity sold at 17% profit?

Alligation or MixtureSolution: 7 17 10 (17-10) (10-7) 7 : 3The quantity of 2nd kind = 3/10 of 100kg = 30kg

Alligation or MixtureIn what ratio two varieties of tea one costing Rs. 27 per kg and the other costing Rs. 32 per kg should be blended to produce a blended variety of tea worth Rs. 30 per kg. How much should be the quantity of second variety of tea, if the first variety is 60 kg?

Alligation or MixtureSolution:27323023Quantity of cheaper tea=2Quantity of superior tea3

Quantity of cheaper tea =2*x/5 = 60 , x=150Quantity of superior tea = 3 * 150/5 = 90 kg

Alligation or MixtureA man buys two cows for Rs. 1350 and sells one so as to lose 6% and the other so as to gain 7.5% and on the whole be neither gains nor loss. What does each cow cost?

Alligation or MixtureSolution:-67.5 07.56Ratio = 5 : 4Cost of first cow = 1350*5/9=Rs. 750Cost of second cow = Rs. 600


Three types of tea A,B,C costs Rs. 95/kg, Rs. 100/kg. and Rs 70/kg respectively. How many kg of each should be blended to produce 100 kg of mixture worth Rs.90/kg given that the quantities of B and C are equal?Sathyam Question

Alligation or MixtureAnswer:B+C/2A85959055Ratio is 1:1 so A = 50 , B + C = 50

The quantity would be 50 : 25 : 25

Alligation or MixtureIn what proportion water must be added to spirit to gain 20% by selling it at the cost price?

Alligation or MixtureSolution:Profit%=20%Let C.P =S.P= Rs.10 Then CP=100/(100+P%)SP =25/3

010 25/35/325/3

The ratio is 1: 5

Chain RuleDirect Proportion : A B A BIndirect Proportion: A B A B

Chain RuleIf 36 men can do a piece of work in 25 days then in how many days 15 men will do it?

Chain RuleSolution:MenDays362515x(Indirect)x = 36 * 25/15x = 60 days

Chain RuleIf 12 carpenters working 6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?

Chain RuleSolution:

MenDaysHoursChairs1224646018368x x/460=18*8*36/12*6*24x=1380They will make 1380 chairs.

Chain RuleIf 1 man can load 1 box in a truck in 9 minutes and a truck can hold up to 8 boxes. How many trucks completely are loaded when 18 men work for 1.5 hours? ( CTS )

Chain RuleSolution:MenBoxMinTrucks119118890x

x = 18 *1* 90/1*8 * 9 = 22.5The number of trucks completely loaded = 22

Chain RuleA garrison of 3300 men has provisions for 32 days when given at a rate of 850 grams per head. At the end of 7 days reinforcement arrives and it was found that now the provisions will last 8 days less when given at the rate of 825 grams per head. How many more men can it feed?(Sathyam question)

Chain RuleSolution:MenDaysGrams330017850x25825x = 3300 * 25 * 850/17 * 825 = 50005000 3300 = 1700It can feed 1700 more men.

Chain RuleIf 3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day. How many days will it take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day?

Chain RuleSolution:One mans work = 2 boys workSo, 6 men and 2 boys = 6 (2) + 2 = 14 boysBoysHoursDaysWork67101148x2x = 6 * 7 * 10 * 2/14 * 8They will finish the work in 7 days.

Partnership

Types: A invested Rs.x and B invested Rs.y then A : B = x : yA invested Rs.X and after 3 months B invested Rs.Y then the share isA : B = X * 12 : Y * 9

PartnershipA and B are two partners in a business. A contributes Rs. 1200 for 5 months and B Rs. 750 for 4 months. If total profit is Rs. 450, find the respective shares.

PartnershipSolution:Ratio is1200 * 5 : 750 * 4 = 2 : 1

Profit share of A = 2/3 * 450 = Rs. 300

Profit share of B = Rs. 150

PartnershipA and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and As share is Rs. 855, what is the total profit %?

PartnershipSolution:Let the total profit be Rs. 100After paying charity As share = 3/5 *95 = 57If As share is Rs. 57, the total profit is 100If As share is Rs. 855, the total profit is 100 * 855/57 = Rs. 1500The total profit = Rs. 1500

PartnershipA,B,C entered into a partnership by making an investment in the ratio of 3 : 5 : 7. After a year C invested another Rs. 337600 while A withdrew Rs. 45600. The ratio of investments then changed into 24: 59 : 167. How much did A invest initially?

PartnershipSolution:Let the investments of A, B, and C be 3x, 5x, 7x(3x 45600) : 5x : (7x + 337600) = 24 : 59 : 167(3x 45600)/5x = 24/59x = 47200Initial investment of A = 47200 * 3 = Rs. 141600

Partnership

A,B,C started a business each investing Rs. 20000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invested Rs. 6000 more. At the end of the year a total profit of Rs. 69900 was recorded. Find the share of each.(Satyam Question)

Partnership

Solution:(20000*5+15000*7) : (20000*5+16000*7) : (20000*5 + 26000*7)The ratio is 205 : 212: 282As share = 205/699 * 69900 = Rs. 20500Bs Share = Rs. 21200Cs share = Rs. 28200

Partnership

A starts business with a capital of Rs. 1200. B and C join with some investments after 3 and 6 months respectively. If at the end of a year the profit is divided in the ratio 2 : 3 : 5 respectively what is Bs investment in the business?

Partnership

Solution:(1200 * 12) : ( x * 9) : (y * 6) = 2 : 3 : 5

(1200 * 12)/2 = 9x/3x = 2400Bs investment = Rs. 2400

PartnershipA and B enter into partnership for a year. A contributes Rs.1500 and B Rs. 2000. After 4 months, they admit C who contributes Rs. 2250. If B withdraws his contribution after 9 months, find their profit share at the end of the year? (In the ratio)

PartnershipSolution:A: B: C = 1500*12: 2000*9: 2250*8 = 18000: 18000: 18000 = 1: 1: 1Profit share at the end of the year = 1: 1: 1

Time and WorkIf A can do a piece of work in n days, then As 1 days work = 1/nIf A is thrice as B, then: Ratio of work done by A and B = 3:1 Ratio of times taken by A and B= 1:3

Pipes and Cisterns

P1 fills in x hrs. Then part filled in 1 hr is 1/x

P2 empties in y hrs. Then part emptied in 1 hr is 1/y

Pipes and Cisterns P1 and P2 both working simultaneously which fills in x hrs and empties in y hrs resp ( y>x) then net part filled is 1/x 1/y

P1 can fill a tank in X hours and P2 can empty the full tank in y hours( where x>y), then on opening both pipes, the net part empties in hour 1/y -1/x

Time and WorkA can do a piece of work in 8 days. A undertook to do it for Rs. 320. With the help of B, he finishes the work in 6 days. Find Bs share.

Time and WorkSolution:(A + B)s 1 day work = 1/6As 1 day work = 1/8Bs 1 day work = 1/24Ratio of their work = 3 : 1B gets * 320 = Rs. 80

Time and Work5 men or 8 women do equal amount of work in a day. A job requires 3 men and 5 women to finish the job in 10 days. How many women require to finish the job in 14 days?Satyam Question

Time and WorkSolution:5 men = 8 women, so 1 man = 8/5 women3m + 5w = 3 (8/5) w + 5 w = 49/5 wDaysWomen1049/514xThe number of women required = 7

Time and WorkA can do a piece of work in 30 days, and B in 50 days and C in 40 days. If A is assisted by B on one day and by C on the next day alternatively work will be completed in ?

Time and WorkSolution:A = 1/30, B = 1/50, C = 1/40A+B = 1/30+1/50 = 8/150A+C = 1/30+1/40 = 7/1202 days work done by A & B = 8/150 + 7/120) = 67/60016 days work done = 67 * 8/600 = 536/600 = 67/75Work left = 1-67/75 = 8/7517th day A & B are working = 8/75 8/150 = 4/75 18th day A&C are working 4/75 = 120/7* 4/75 = 32/35They will finish the work in 17 + 32/35 = 17 32/35 days

Time and WorkTwo men undertake to do a piece of work for Rs.1400. First man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should money be divided?

Time and WorkSolution:Wages of the first man for 3 days= work done by him in 3 days * Rs. 1400= 3/7 * 1400 = Rs. 600Wage of second man for 3 days = work done by him in 3 days * Rs. 1400 = 3 / 8 *1400 = Rs. 525Wages of the boy for 3 days = Rs. 1400 Rs. (600 + 525) = Rs. 275 There shares will be 600, 525, 275.

Time and Work2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?Satyam Question

Time and WorkAnswer:1 mans work = x1 boys work = y2x + 3y = 1/10and 3x + 2y = 1/8Solving the above equations,The required number of days = 12 days

Time and Work (Pipes)

Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern then find the time in which A and B will fill the cistern separately.

Time and Work (Pipes)Answer:1/x + 1/(x+5) = 1/6

Solving the above equation,Pipe A will fill the cistern in 10 minutes.Pipe B will fill the cistern in 15 minutes.

Time and Work (Pipes)A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is filled in 20 minutes. How long will a waste pipe take to empty a full cistern ?

Time and Work (Pipes)Solution:All the tap work together = 1/12 + 1/15 - 1/20 = 5/60 + 4/60 3/60 = 6/60 = 1/10 The waste pipe can empty the cistern in 10 minutes.

Time and Work (Pipes)One fill pipe A is 3 times faster than second fill pipe B and takes 32 minutes less than the fill pipe B. when will the cistern be full if both pipes are opened together ?

Time and Work (Pipes)Solution:B = xA = 3xB = x (1/3) = x/3x 32 =x/33x 96 = x3x x = 962x = 96x = 96/2 = 48B = 48 -32 = 16A and B together = 1/16 + 1/48 = 1/12The cistern will be filled in 12 minutes when both the pipes are opened together.

Time and Work (Pipes) Two pipes A and B can fill a tank in 20 min. and 40 min. respectively. If both the pipes are opened simultaneously, after how much time A should be closed so that the tank is full in 10 minutes?

Time and Work (Pipes) Solution:Let B be closed after x minutes. Then,Part filled by (A+B) in x min + part filled by A in( 10 x min)=1x (1/20 +1/40) + (10 x) * 1/20 = 1x (3/40) + 10 x/20 = 13x/40 + 10 x/ 20 = 13x + 20 2x = 403x 2x = 40 -20x = 20 min. A must be closed after 20 minutes.

Time and Work (Pipes)Two taps A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full?

Time and Work (Pipes)Solution:As work in hour = 1/6, Bs work in 1 hour = 1/4(A + B) s 2 hr work = 1/6+1/4 = 5/12(A + B) s 4 hr work = 10/12 = 5/6Remaining Part = 1- 5/6 = 1/6Now, it is As turn and 1/6 part is filled by A in 1 hour.Total time = 4+1 =5

Area and VolumeCube:Let each edge of the cube be of length a. then,Volume = a3cubic unitsSurface area= 6a2 sq.units.Diagonal = 3 a units.

Area and VolumeCylinder:Let each of base = r and height ( or length) = h. Volume = r2hSurface area = 2 r h sq. unitsTotal Surface Area = 2 r ( h+ r) units.

Area and VolumeCone:Let radius of base = r and height=h, thenSlant height, l = h2 +r2 unitsVolume = 1/3 r2h cubic unitsCurved surface area = r l sq.unitsTotal surface area = r (l +r)

Area and VolumeSphere:Let the radius of the sphere be r. then,Volume = 4/3 r3Surface area = 4 r2sq.units

Area and VolumeCircle: A= r 2 Circumference = 2 r Square: A= a 2 Perimeter = 4aRectangle: A= l x bPerimeter= 2( l + b)

Area and VolumeTriangle:A = 1/2*base*heightEquilateral = 3/4*(side)2 Area of the Scalene Triangle S = (a+b+c)/ 2 A = s*(s-a) * (s-b)* (s-c)

Area and Volume

What is the cost of planting the field in the form of the triangle whose base is 2.8 m and height 3.2 m at the rate of Rs.100 / m2

Area and VolumeSolution:Area of triangular field = * 3.2 * 2.8 m2 = 4.48 m2 Cost = Rs.100 * 4.48 = Rs.448..

Area and VolumeFind the length of the longest pole that can be placed in a room 14 m long, 12 m broad, and 8 m high.

Area and VolumeSolution:Length of the longest pole = Length of the diagonal of the room = (142 + 122 + 82) = 404= 20.09 m

Area and Volume

Area of a rhombus is 850 cm2. If one of its diagonal is 34 cm. Find the length of the other diagonal.

Area and VolumeSolution: 850 = * d1 * d2 = * 34 * d2 = 17 d2 d2 = 850 / 17 = 50 cm Second diagonal = 50cm

Area and VolumeA grocer is storing small cereal boxes in large cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each small cereal box is 7 inches by 6 inches by 5 inches then what is maximum number of small cereal boxes that can be placed in each large carton ?

Area and VolumeSolution: No. of Boxes = 25*42*60 / 7*6*5 = 300300 boxes of cereal box can be placed.

Area and Volume

If the radius of a circle is diminished by 10%, what is the change in area in percentage?

Area and VolumeSolution:= x + y + xy/100= -10 - 10 + 10*10/100= -19% Diminished area = 19%.

Area and Volume

A circular wire of radius 42 cm is bent in the form of a rectangle whose sides are in the ratio of 6:5. Find the smaller side of the rectangle?

Area and VolumeSolution:length of wire = 2 r = (22/7*14*14)cm = 264cmPerimeter of Rectangle = 2(6x+5x) cm = 22xcm 22x =264 x = 12 cm Smaller side = (5*12) cm = 60 cm

Area and VolumeA farmer owns a square field with a pole in one of the corners to which he tied his cow with a rope whose length is about 10 m. What is the area available for the cow to graze?(Caritor Question)

Area and VolumeAnswer:

Area = 78.5 m2

Area and Volume

If the length of a rectangle is reduced by 20% and breadth is increased by 20%. What is the percentage change in the area?

(Infosys Question)

Area and VolumeSolution:x + y + (xy/100)%= - 20 + 20 400/100= -4The area would decrease by 4%

Area and VolumeA power unit is there by the bank of the river of 750 m width. A cable is made from power unit to power a plant opposite to that of the river and 1500 m away from the power unit. The cost of the cable below water is Rs. 15 per meter and cost of cable on the bank is Rs. 12 per meter. Find the total cost.(TCS Question)

Area and VolumeAnswer: Cable under water is 750m, on the bank 750m(750 * 15) + (750 * 12) = 20250 Total cost = Rs. 20250

ProbabilityProbability: P(E) = n(E) / n (S)Addition theorem on probability: n(AUB) = n(A) + n(B) - n(AB)Mutually Exclusive: P(AUB) = P(A) + P(B) Where P(A B)=0Independent Events: P(AB) = P(A) * P(B)

Probability

There are 6 pairs of gloves of different sizes. In how many ways can you choose one for the left hand and one for the right hand such that they are not of the same pair?(Caritor Question)

ProbabilitySolution:

The number of possibilities are 6 * 6 = 36They should not be from the same pair = 36 - 6 =30 30 ways.

Probability

A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time?(Wipro Question)

ProbabilityAnswer :P(Both tell truth) = P(A) * P (B)= 0.8 * 0.6 P = 0.48

Probability

A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group find the probability for the selected person to be an employee.(Satyam Question)

ProbabilitySolution:Let the number of men is 100 and women be 100Employed men and women = (100-10)+(100-45)= 145Probability = 145 / 200 = 29 / 40

Probability The probability of an event A occurring is 0.5 and that of B is 0.3. If A and B are mutually exclusive events. Find the probability that neither A nor B occurs?

ProbabilitySolution:It is Mutually exclusive events P(A n B)=0Probability = 1 ( P(A) + P (B) P(A n B) ) = 1 (0.5 + 0.3 0) = 0.2

Simple / Compound Interest Simple Interest = PNR / 100Amount A = P + PNR / 100When Interest is Compound annually:Amount = P (1 + R / 100)n C.I = A-P

Simple / Compound InterestHalf-yearly C.I.: Amount = P (1+(R/2)/100)2n

Quarterly C.I. :

Amount = P (1+(R/4)/100)4n

Simple/compound interestDifference between C.I and S.I for 2 years = P*(R/100)2.

Difference between C.I and S.I for 3 years = P{(R/100)3+ 3(R/100)2 }

Simple / Compound Interest

If the compound interest on a certain sum for two years is Rs.60.60 and simple interest is Rs. 60, then the rate of interest per annum is ?

Simple / Compound InterestSolution: SI for 2 years60 = P*2*R/100PR/ 100 = 30C.I S.I = P (R/100)2 P(R/100 * R/100) = 0.60 30 * R/100 =0.6 = 2% The rate of interest is 2%

Simple / Compound InterestFind in what time a given sum of money will quadruple itself at simple interest at the rate of one paise per rupee per month ?

Simple / Compound InterestSolution:4P after n years4P = P+ P*n*12/1004 = 1+ 12n/100n = 25 yearsThe period is 25 years.

Simple / Compound InterestIf Rs. 1000 is invested at 5% simple interest if the interest is added to the principal every ten years, the amount will become Rs. 2000 after how many years ?

Simple / Compound InterestSolution:Amount = Principle + interest for 10 years = 1000 +( 1000*10*5/100 ) = 15001500 after 10 years2000 after n years500 = 1500*5*n/100 n = 6 2/3yearTotal 10 + 6 2/3 = 16 2/3 Total time is 16 2/3 years

Simple/compound interest

A sum of money amounts to Rs. 6690 after 3 years and to Rs. 10035 after 6 years on C.I. Find the sum.

(Satyam Question)

Simple/Compound interestSolution:P(1 + R/100)3= 6690 -----------1P(1 + R/100)6= 10035 -----------2Dividing(1 + R/100)3 = 10035/6690 = 3/2Substitute in equation 1 then P(3/2)=6690P = 6690 * 2/3 = 4460 The sum is Rs.4460

Simple/Compound interestWhat will be the difference between S.I and C.I on a sum of Rs. 4500 put for 2 years at 5% per annum?

Simple/Compound interestSolution:C.I S.I = P (R/100)2

Difference = Rs. 11.25

AverageAverage is a simple way of representing an entire group in a single value.Average of a group is defined as: X = (Sum of items) / (No of items)

AverageA batsman makes a score of 90 runs in the 17th innings and then increases his average by 3. Find his average after 17th innings.(Infosys Question)

AverageSolution: Let the average of 17th innings be xAverage after the 16th innings = x-316(x-3) + 90 = 17xx = 42

Average

The average of 11 observations is 60. If the average of 1st five observations is 58 and that of last five is 56, find sixth observation?

AverageSolution:5 observations average = 58Sum = 58*5 = 290Last 5 observation average = 56Sum = 56*5 = 280Total sum of 10 numbers = 570 (290 + 280)Total sum of 11 numbers = 660 (11*60)6th number = 90 (660 570)

Average

The average of age of 30 students is 9 years. If the age of their teacher included, it becomes 10 years. Find the age of the teacher?

AverageSolution:30 students total age = 30*9=270

Including the teachers age = 31*10=310

Difference = 310 270 = 40 years

AverageOf the three numbers second is twice the first and is also thrice the third. If the average of the three numbers is 44, find the largest number.

AverageAnswer:Let the first number be x

Average = (x + 2x + 2x/3)/3 = 44

Largest number is 72

AverageIn a coconut groove, (x+2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x-2) trees yield 180 nuts per year. If the average yield per year per tree be 100 find x.

AverageAnswer:[(x+2)*60 + (x*120) + (x-2) *180] =100 [x+2+x+x-2]By simplifyingx = 4

AverageIn a cricket team of 11 boys one player weighing 42 kg is injured and his place is taken by another player. If the average weight of the team is increased by 100 g as a result of this, then what is the weight of the new player?

AverageSolution: Average weight of 11 boys is increased by 0.1 kg

The total increase in weight = 0.1 * 11 = 1.1 kg

Weight of the new boy = 42 + 1.1 = 43.1 kg

Permutations and CombinationsFactorial Notation: n! = n(n-1)(n-2).3.2.1 Number of Permutations: n! / (n-r)!

Combinations: n! / r!(n r)!

Permutations and CombinationsThe number of Combinations of n things taken r at a time in which p particular things will always occur is n-pCr-pThe number of Combinations of n things taken r at a time in which p particular things never occur is n-pCr

Permutations and CombinationsA foot race will be held on Saturday. How many different arrangements of medal winners are possible if medals will be for first, second and third place, if there are 10 runners in the race

Permutations and CombinationsSolution:n = 10r = 3n P r = n!/(n-r)! = 10! / (10-3)! = 10! / 7! = 8*9*10 = 720 Number of ways is 720.

To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants, and two managers from 4 applicants. What is total number of ways in which she can make her selection ?Permutations and Combinations

Permutations and CombinationsSolution:It is selection so use combination formulaProgrammers and managers = 6C3 * 4C2 = 20 * 6 = 120Total number of ways = 120 ways.

Permutations and CombinationsA man has 7 friends. In how many ways can he invite one or more of them to a party?

Permutations and CombinationsSolution: In this problem, the person is going to select his friends for party, he can select one or more person, so addition = 7C1 + 7C2+7C3 +7C4 +7C5 +7C6 +7C7 = 127 Number of ways is 127

Permutations and Combinations

If nP5 = 20 nP3 then what is the value of n?

Permutations and CombinationsSolution:

n!/(n-5)! = 20 * n!/(n-3)!

n = 8

Permutations and CombinationsFind the number of different 8 letter words formed from the letters of the word EQUATION if each word is to start with a vowel

Permutations and CombinationsSolution:For the words beginning with a vowel, the first letter can be any one of the 5 vowels, the remaining 7 places can be filled by7P7= 5040The number of words = 5 * 5040 = 25200

Permutations and CombinationsIn how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?

Permutations and CombinationsSolution:A,I,E can be arranged in 3! Ways

(5! * 3!) / 2! = 360 ways

Percentage By a certain Percent, we mean that many hundredths. Thus, x Percent means x hundredths, written as x%

Finding out of Hundred.If Length is increased by X% and Breadth is decreased by Y% What is the percentage Increase or Decrease in Area of the rectangle? Formula: X+Y+ XY/100 % Decrease 20% means -20

Percentage

Percentage

Two numbers are respectively 30% & 40% less than a third number. What is second number as a percentage of first?

PercentageSolution:Let 3rd number be x.1st number = x 30% of x = x 30x/100 = 70x/ 100 = 7x/102nd number = x 40% of x = x 40x/100 = 60x/ 100 = 6x/10Suppose 2nd number = y% of 1st n umber6x / 10 = y/100 * 7x /10 y = 600 / 7 y = 85 5/7 85 5/7%

PercentageAfter having spent 35% of the money on machinery, 40% on raw material, 10% on staff, a person is left with Rs.60,000. The total amount of money spent on machinery and the raw material is?

PercentageSolution:Let total salary =100%Salary = 100Spending: Machinery + Raw material + staff = 35+40+10 = 85Remaining percentage = 100 85 = 1515 = 60000100 = ? By chain rule, we get 400000In this 400000 , 75% for machinery & raw material = 4, 00,000* 75/100 =Rs 3 00000

PercentageIf the number is 20% more than the other, how much percent is the second number less than the first?

Percentage

Solution:Let x =20 = x / (100+x) *100 =( 20 /120 )*100 =16 2/3 The percentage is 16 2/3

PercentageSolution:Let capacity of the tank be 100 liters. Then,Initially: A type petrol = 100 litersAfter 1st operation:A = 100/2 = 50 liters, B = 50 litersAfter 2nd operation:A = 50 / 2+50 = 75 liters, B = 50/2 = 25 litersAfter 3rd operation:A = 75/2 37.5 liters, B = 25/2 +50 = 62.5 litersRequired Percentage = 37.5%

PercentageAnswer:Increase % in the area of the new rectangle=x + y + (xy/100)%=20 + 10 + (200/100)=32%Increase 32%

PercentageIf As income is 40% less than Bs income, then how much percent is Bs income more than As income?

PercentageAnswer:

Bs income = 40/(100-40) * 100%= 66 2/3%

Percentage

Ramesh loses 20% of his pocket money. After spending 25% of the remainder he has Rs. 480 left. What was his pocket money?

PercentageAnswer:

x (1-20/100) (1-25/100) = 480

Solving the equation, x = 800

Pocket money = Rs. 800

Boats and streamsUp stream against the streamDown stream along the streamu = speed of the boat in still water v = speed of stream Down stream speed (a)= u+v km / hrUp stream speed (b)=u-v km / hru = (a+b) km/hrV = (a-b) km / hr

Boats and streamsA boats crew rowed down a stream from A to B and up again in 7 hours. If the stream flows at 3km/hr and speed of boat in still water is 5 km/hr. , find the distance from A to B ?

Boats and streamsSolution: Down Stream = Sp. of the boat + Sp. of the stream = 5 +3 =8Up Stream = Sp. of the boat Sp. of the stream = 5-3 = 2Let distance be xDistance/Speed = Time X/8 + x/2 = 7 X/8 +4x/8 = 15/2 5x / 8 = 15/2 5x = 15/2 * 8 x =12

Boats and StreamsA boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. Find the speed of the boat in still water in km/hr?

Boats and StreamsSolution: Speed of the boat in upstream = 40/8 = 5 km/hr Speed of the boat in downstream = 36/6 = 6 km/hr Speed of the boat in still water = 5+6/2 = 5.5 km/hr

Boats and Streams

A man rows to place 48km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of the stream?

Boats and StreamsSolution:Down stream 4km in x hours. Then,Speed of Downstream = 4/x km/hr, Speed of Upstream = 3/x km/hr48/ (4/x) + 48/(3/x) = 14 , x = 1/2Speed of Down stream = 8, Speed of upstream = 6Rate of the stream = (8-6) km/hr = 1 km/hr

Boats and Streams

In a stream running at 2 km/h a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the motor boat in still water.

Boats and StreamsSolution:Let the speed be x km/h10/(x+2) + 10/(x-2)=55/60Solving the above equation,x = 22 km/h

Boats and StreamsA swimmer can swim a certain distance in the direction of current in 5 hours and return the same distance in 7 hours. If the stream flows at the rate of 1 km/h, find the speed of the swimmer in still water.

Boats and StreamsSolution:Let the speed of the swimmer in still water be xDownstream speed = (x+1) * 5Upstream speed = (x-1) * 75(x+1) = 7(x-1)Solving the equation, x = 6Speed of the swimmer = 6 km/h

Time and DistanceSpeed:- Distance covered per unit time is called speed.Speed = distance/time Distance = speed*time Time = distance/speed

Time and Distance Distance covered Time (direct variation).

Distance covered speed (direct variation).

Time 1/speed (inverse variation).

Time and DistanceSpeed from km/hr to m/sec - ( * 5/18).

Speed from m/sec to km/h, - ( * 18/5).

Average Speed:- Average speed = Total distance traveled Total time taken

Time and DistanceThe jogging track in a sports complex is 726m in circumference. Suresh and his wife start from the same point and walk in opposite direction at 4.5km/hr and 3.75km/hr respectively. They will meet for the first time in how many minutes ?

Time and DistanceSolution: Suresh speed m/hr = 4.5*5/18 *60*60 = 4500 His wife speed m/hr = 3.75*5/18*60*60 = 3750 Meeting time 4500/60 x +3750/60x = 756 m x = 5.28 m They will meet after 5.28minutes

Time and DistanceRam travels from P to Q at 10km/hr and returns at 15km/hr. Shyam travels P to Q and returns at 12.5km/hr. If he takes 12 minutes less than ram then what is the distance between P and Q ?

Time and DistanceSolution:Average Speed of Ram = 2(10*15)/25 = 12km/hrAverage Speed of Shyam = 2(12.5 *12.5)/25 = 12.5Rams speed in m/sec = 12*5/18 = 10/3Shyams speed in m/sec = 12.5*5/18 = 625/36(x/ 10/3) (x/625/36) = 12*60 3x/10 30x/625 = 720 = 30 Distance between P and Q is 30 km

Time and DistanceIf I walk 30 miles/hr I reach 1 hour before and if I walk 20 miles/hr I reach 1 hour late. Find the distance between two points and if the exact time of reaching destination is 11 a.m. then find the speed with which I walk?Infosys Question

Time and DistanceSolution:x/30-x/20 = 2By Solving the equation,The total distance between two points = 120 milesTheAverage speed required = 24 miles/hr

Time and DistanceBy walking at of his usual speed, a man reaches office 20 minutes later than usual. Find his usual time?

Time and DistanceSolution: Usual time = Numerator * late time = 3*20 = 60

Time and DistanceA car travels a certain distance taking 7 hours in forward journey. During the return journey it increased the speed by 12 km/hr and takes the time of 5 hours. What is the distance traveled?

(Satyam Question)

Time and DistanceSolution:Let speed be x , D = S * T =7x7x = (x+12) 5Solving the above equation,x = 30D = 7 * 30 = 210Actual Distance = 210 km

Time and Distance (Trains)A train starts from Delhi to Madurai and at the same time another train starts from Madurai to Delhi after passing each other they complete their journeys in 9 and 16 hours, respectively. At what speed does second train travels if first train travels at 160 km/hr ?

Time and Distance (Trains)Solution:Let x be the speed of the second trainS1 / S2 = T2/T1160/x = 16/9160/x = 4/3 x = 120The speed of second train is 120km/hr.

Time and Distance (Trains)

How long will a train 100 m long traveling at 72 km/hr take to overtake another train 200 m long traveling at 54 km/h?(Satyam Question)

Time and Distance (Trains)Solution:They are traveling in the same direction. Hence the Relative speed is x -y72 54 = 18 km/h18 * 5/18 = 5 m/secTo travel 5 m it takes 1 secondTo travel 300m it will take300/5 = 60 secondsIt will take 60 seconds or 1 minute.

Time and Distance (Trains)Rajee starts her journey from Delhi to Bhopal and simultaneously Sheela starts from Bhopal to Delhi. After crossing each other they finish their remaining journey in 5 4/9 hours and 9 hours respectively. What is Sheelas speed if Rajees speed is 36 km/hr.

Time and Distance (Trains)Answer:Rajees speed= Square root of (t2/t1)Sheelas speed

The speed of Sheela = 28 km/hr

Time and Distance (Trains)Excluding stoppages, the speed of a train is 54 km/hr and including stoppages it is 45 km/hr. For how many minutes does the train stop per hour?

Time and Distance (Trains)Solution: x = _____________ x/45 + x/36Take L.C.M and find the x value x = 12 It stops 12 minutes/hr

Time and Distance (Trains)A train 130 m long passes a bridge in 21 seconds moving with a speed of 90 km/hr. Find the length of the bridge?

Time and Distance (Trains)Solution:Let the length of the bridge be xSpeed of the train = (length of the train + length of the bridge) / Time taken90*5/18 = (130 +x )/21Length of the bridge = 395 m

Profit and LossGain =(S.P.)-(C.P.)Loss =(C.P.)-(S.P.)Loss or gain is always reckoned on C.P.Gain% = [(Gain*100)/C.P.]Loss% = [(Loss*100)/C.P.]S.P. = ((100 + Gain%)/100)C.P.S.P. = ((100 Loss%)/100)C.P.

Profit and LossSundeep buys two CDs for Rs.380 and sells one at a loss of 22% and the other at a gain of 12%. If both the CDs are sold at the same price, then the cost price of two CDs is ?

Profit and LossSolution:CDs =Rs.3801st CD = x -22x/1002nd CD = y + 12y/100SP1 = SP2x 22x/100 = y 12y/100 x = 56y/39 x + y = 380 56y/39 + y = 380 y = 156 x = 224 Cost of the two CDs are Rs. 224 and Rs.156

Profit and Loss

Mr. Ravi buys a cooler for Rs. 4500. For how much should he sell so that there is a gain of 8%

Profit and LossSolution:S.P = (100+8%/100)/CP= (108/100) * 4500 = 4860He should sell it for Rs. 4860.

Profit and Loss If the manufacturer gains 20%, the wholesale dealer 25%, and the retailer 35%, then find the cost of production if the retail price is Rs. 1265.

Profit and LossSolution:Let C.P be x

Gain35% of 25% of 20% of x = 1265135/100 * 125/100 * 120/100 * x = 1265

x = Rs.624.7

Profit and Loss

Manoj sells a shirt to Yogesh at a profit of 15% and Yogesh sells it to Suresh at a loss of 10%. Find the resultant profit or loss.

Profit and LossSolution:Resultant profit = (x + y + xy/100)= 15 10 (150/100)= 3%

The resultant profit is 3.5%

Profit and Loss

Mr. Verma sold his scooter for Rs. 10500 at a gain of 5%. Find the cost price of the scooter.

Profit and LossSolution:

C.P = (100/(100+P%))*S.P= (100/(100+5) )* 10500= 10000Cost price = Rs. 10000

Profit and LossA man bought a horse and a cart. If he sold the horse at 10% loss and the cart at 20% gain, he would not lose anything, but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. What is the cost of one horse and one cart?Satyam Question

Profit and LossSolution : C.P of horse = x; C.P of cart = y

10x/100 = 20y/1005x/100 = 5y/100 + 10Solving the above two equations,C.P of horse = x = Rs. 400C.P of cart = y = Rs. 200

Profit and LossA man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs. 10.50 less he would have gained 30%. Find the cost price of the article.

Satyam Question

Profit and LossSolution:First C.P = x, S.P = 125% of x = 5x/4Second C.P = 80x/100 = 4x/5S.P= 130/100 * 4x/5 = 26x/55x/4 - 26x/25 = 10.50x = 50The cost price is Rs. 50

CalendarOdd days:0 = Sunday1 = Monday2 = Tuesday3 = Wednesday4 = Thursday5 = Friday6 = Saturday

CalendarMonth code: Ordinary yearJ = 0 F = 3M = 3 A = 6M = 1 J = 4J = 6 A = 2S = 5 O = 0N = 3 D = 5 Month code for leap year after Feb. add 1.

CalendarOrdinary year = (A + B + C + D )-2 -----------------------take remainder 7

Leap year = (A + B + C + D) 3 ------------------------- take remainder 7

Calendar

What is the day of the week on 30/09/2007?

CalendarSolution:A = 2007 / 7 = 5B = 2007 / 4 = 501 / 7 = 4C = 30 / 7 = 2D = 5 ( A + B + C + D )-2 = ----------------------- 7 = ( 5 + 4 + 2 + 5) -2 ----------------------- = 14/7 = 0 = Sunday 7

CalendarWhat was the day of the week on 13th May, 1984?

CalendarSolution:A = 1984 / 7 = 3B = 1984 / 4 = 496 / 7 = 6C = 13 / 7 = 6D = 2 ( A + B + C + D) -3 = ----------------------- 7 = 14/7= 0, Sunday.

Calendar

On what dates of April 2005 did Sunday fall?

CalendarSolution: You should find for 1st April 2005 and then you find the Sundays date.A = 2005 / 7 = 3B = 2005 / 4 = 501 / 7 = 4C = 1 / 7 = 1D = 6 (A + B + C + D) -2 = ----------------------- 7 3 + 4 + 1 + 6 -2 ----------------------- = 12 / 7 = 5 = Friday. 7 1st is Friday means Sunday falls on 3, 10, 17, 24

Calendar

What was the day on 5th January 1986?

CalendarSolution:

A = 1986 / 7 = 5B = 1986 / 4 = 496/7 = 6C = 5 / 7 = 5D = 0 (A + B + C + D) -2 = ----------------------- 7 5 + 6 + 5 + 0-2 = ----------------------- = 14 / 7 = Sunday 7

Clocks Clock:In every minute, the minute hand gains 55 minutes on the hour handIn every hour both the hands coincide once. = (11m/2) 30h (hour hand to min hand) = 30h (11m/2) (min hand to hour hand)If you get answer in minus, you have to subtract your answer with 360 o

Clocks

Find the angle between the minute hand and hour hand of a clock when the time is 7:20.

Clocks Solution: = 30h (11m/2) = 30 (7) 11 20/2 = 210 110 = 100Angle between 7: 20 is 100o

Clocks

How many times in a day, the hands of a clock are straight?

ClocksSolution:

In 12 hours, the hands coincide or are in opposite direction 22 times a day.


Clocks

How many times do the hands of a clock coincide in a day?

ClocksSolution:



Clocks

At what time between 7 and 8 oclock will the hands of a clock be in the same straight line but, not together?

ClocksSolution:h = 7 = 30h 11m/2180 = 30 * 7 11 m/2On simplifying we get ,5 5/11 min past 7

Clocks

At what time between 5 and 6 oclock will the hands of a clock be at right angles?

ClocksSolution:h = 5 90 = 30 * 5 11m/2Solving10 10/11 minutes past 5

Clocks

Find the angle between the two hands of a clock at 15 minutes past 4 oclock

ClocksSolution:

Angle = 30h 11m/2 = 30*4 11*15 / 2The angle is 37.5o

Clocks

At what time between 5 and 6 oclock are the hands of a clock together?

ClocksSolution: h = 5

O = 30 * 5 11m/2 m = 27 3/11Solving

27 3/11 minutes past 5

Data InterpretationIn interpretation of data, a chart or a graph is given. Some questions are given below this chart or graph with some probable answers. The candidate has to choose the correct answer from the given probable answers.

1. The following table gives the distribution of students according to professional courses:__________________________________________________________________ Courses Faculty ___________________________________ Commerce Science Total Boys girls Boys girls___________________________________________________________Part time management 30 10 50 10 100C. A. only 150 8 16 6 180Costing only 90 10 37 3 140C. A. and Costing 70 2 7 1 80__________________________________________________________________On the basis of the above table, answer the following questions:

Data InterpretationThe percentage of all science students over Commerce students in all courses is approximately: (a) 20.5 (b) 49.4 (c) 61.3 (d) 35.1

Data InterpretationAnswer:

Percentage of science students over commerce students in all courses = 35.1%

Data InterpretationWhat is the average number of girls in all courses ? (a) 15 (b) 12.5 (c) 16 (d) 11


Average number of girls in all courses = 50 / 4 = 12.5

Data InterpretationWhat is the percentage of boys in all courses over the total students? (a) 90 (b) 80 (c) 70 (d) 76


Percentage of boys over all students = (450 x 100) / 500 = 90%

Data SufficiencyFind given data is sufficient to solve the problem or not.If statement I alone is sufficient but statement II alone is not sufficientIf statement II alone is sufficient but statement I alone is not sufficientIf both statements together are sufficient but neither of statement alone is sufficient.If both together are not sufficient

Data SufficiencyWhat is Johns age?In 15 years will be twice as old as Dias would beDias was born 5 years ago. (Wipro)

Data SufficiencyAnswer: c) If both statements together are sufficient but neither of statement alone is sufficient.

Data SufficiencyWhat is the distance from city A to city C in kms?City A is 90 kms from city B.City B is 30 kms from city C

Data SufficiencyAnswer:

d) If both together are not sufficient

Data SufficiencyIf A, B, C are real numbers, Is A = C? A B = B CA 2C = C 2B

Data SufficiencyAnswer:D . If both together are not sufficient

Data SufficiencyWhat is the 30th term of a given sequence?The first two term of the sequence are 1, The common difference is -1/2

Data SufficiencyAnswer:If statement I alone is sufficient but statement II alone is not sufficient

Data SufficiencyWas Avinash early, on time or late for work?He thought his watch was 10 minute fast.Actually his watch was 5 minutes slow.

Data SufficiencyAnswer:D. If both together are not sufficient

Data SufficiencyWhat is the value of A if A is an integer?A4 = 1A3 + 1 = 0

Data SufficiencyAnswer:B. If statement II alone is sufficient but statement I alone is not sufficient

CubesA cube object 3*3*3 is painted with green in all the outer surfaces. If the cube is cut into cubes of 1*1*1, how many 1 cubes will have at least one surface painted?

CubesAnswer:3*3*3 = 27All the outer surface are painted with colour. 26 One inch cubes are painted at least one surface.

CubesA cube of 12 mm is painted on all its sides. If it is made up of small cubes of size 3mm, and if the big cube is split into those small cubes, the number of cubes that remain unpainted is

CubesAnswer:

= 8

CubesA cube of side 5 cm is divided into 125 cubes of equal size. It is painted on all 6 sides.How many cubes are coloured on only one side?How many cubes are coloured on only two side? How many cubes are coloured on only three side?How many cubes are not coloured?

CubesAnswer:5436827

CubesA cube of 4 cm is divided into 64 cubes of equal size. One side and its opposite side is coloured painted with orange. A side adjacent to this and opposite side is coloured red. A side adjacent to this and opposite side is coloured green?Cont..

CubesHow many cubes are coloured with Red alone?How many cubes are coloured orange and Red alone?How many cubes are coloured with three different colours?How many cubes are not coloured?How many cubes are coloured green and Red alone?

CubesAnswer:88888

CubesA 10*10*10 cube is split into small cubes of equal size 2*2*2 each. A side and adjacent to it is coloured Pink. A side adjacent to Pink and opposite side is coloured Blue. The remaining sides are coloured yellow.Find the no. of cubes not coloured?Find the no. of cubes coloured blue alone?Find the no. of cubes coloured blue & pink & yellow?Find the no. of cubes coloured blue & pink ? Find the no. of cubes coloured yellow & pink ?

CubesAnswer:271841212

Venn DiagramIf X and Y are two sets such that X u Y has 18 elements, X has 8 elements, and Y has 15 elements, how many element does X n Y have?

Venn DiagramSolution:We are given n (X uY) = 18, n (X) = 8, n (Y) =15. using the formula. n( X n Y) = n (X) + n (Y) - n ( X u Y) n( X n Y) = 8 + 15 18n( X n Y) = 5

Venn DiagramIf S and T are two sets such that S has 21elemnets, T has 32 elements, and S n T has 11 elements, how many element elements does S u T have?

Venn DiagramAnswer:n (s) = 21, n (T) = 32, n ( S n T) = 11, n (S u T) = ?n (S u T) = n (S) + n( T) n (S n T) = 21 + 32 11 = 42

Venn DiagramIf A and B are two sets such that A has 40 elements, A u B has 60 elements and A n B has 10 elements, how many element elements does B have?

Venn DiagramAnswer: n ( A) = 40, n ( n B) = 60 and n ( A n B) = 10, n ( A u B) = n ( A) + n (B) n ( A n B) 60 = 40 + n (B) 10 n (B) = 30

Venn DiagramIn a group of 1000 people, there are 750 people who can speak Hindi and 400 who can speak English. How many can Speak Hindi only?

Answer: n( H u E) = 1000, n (H) = 750, n (E) = 400, n( H u E) = n (H) + n (E) n( H n E)1000 = 750 +400 n ( H n E) n ( H n E) = 1150 100 = 150No. of people can speak Hindi only _ = n ( H n E) = n ( H) n( H n E) = 750 150 = 600

Venn DiagramIn a class of 100 students, the number of students passed in English only is 46, in maths only is 46, in commerce only is 58. the number who passes in English and Maths is 16, Maths and commerce is 24 and English and commerce is 26, and the number who passed in all the subject is 7. find the number of the students who failed in all the subjects.

Venn DiagramSolution:No. of students who passed in one or more subjects = 11+ 9 + 13 + 17 + 15 + 19 + 7 = 91No of students who failed in all the subjects = 100 -91 = 9

Venn DiagramIn a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

Venn DiagramAnswer: 3 of them studied both Latin and Greek.

THANK YOUSreenivasa Chowdary Nellore M.B.A, [Director]NARENS Institute for Competitive Examinations,HYDERABAD.E-mail: [email protected]: + 91 99123 31989, + 91 90593 14623

quantitative ability - level c

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