general aptitude

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GATE-ME

Previous Years Solved Paper

General Aptitude



GATE SOLVED PAPER - ME GENERAL APTITUDE

GATE Previous Year Papers Solved by Team GATESCORE

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YEAR 2013 ONE MARK

Q. 1 Choose the grammatically INCORRECT sentence(A) He is of Asian origin (B) They belonged to Africa

(C) She is an European (D) They migrated from India toAustralia

Q. 2 What will be the maximum sum of ,44 42, ,........?40

(A) 502 (B) 504

(C) 506 (D) 500

Q. 3 Were you a bird, you...................... in the sky.(A) would fly (B) shall fly

(C) should fly (D) shall have flown

Q. 4 Which one of the following options is the closest in meaning to the word givenbelow ?Nadir

(A) Highest (B) Lowest

(C) Medium (D) Integration

Q. 5 Complete the sentence:

Universalism is the particularism as diffuseness is to.................(A) specificity (B) neutrality

(C) generality (D) adaptation

YEAR 2013 TWO MARKS

Q. 6 The current erection cost of a structure is .13,200Rs . If the labour wages per day

increase by /1 5 of the current wages and the working hours decrease by 1/24 ofthe current period, then the new cost of erection in Rs. is(A) 16,500 (B) 15,180

(C) 11,000 (D) 10,120

Q. 7 After several defeats in wars, Robert Bruce went in exile and wanted to commitsuicide. Just before committing suicide, he came across a spider attemptingtirelessly to have its net. Time and again, the spider failed but that did not deterit to refrain from making attempts. Such attempts by the spider made Brucecurious. Thus, Bruce started observing the near-impossible goal of the spider to

have the net. Ultimately, the spider succeeded in having its new despite severalfailures. Such act of the spider encouraged Bruce not to commit suicide. Andthen, Bruce went back again and won many a battle and the rest is history.

Which of the following assertions is best supported by the above information ?(A) Failure is the pillar of success

(B) Honesty is the best policy(C) Life begins and ends with adventures

(D) No adversity justifies giving up hope.

Q. 8 A tourist covers half of his journey by train at 60 /km h, half of the remainderby bus at 30 /km h and the rest by cycle at 10 /km h. The average speed of the

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tourist in km/h during the entire journey is

(A) 36 (B) 30

(C) 24 (D) 18

Q. 9 Find the sum of the expression

...........................1 2

1

2 3

1

3 4

1

80 81

1

++

++

++ +

+

(A) 7 (B) 8

(C) 9 (D) 10

Q. 10 Out of all the 2-digit integers between 1 and 100, a 2-digit number has to beselected at random. What is the probability that the selected number is notdivisible by 7?

(A) 13/90 (B) 12/90(C) 78/90 (D) 77/90

YEAR 2012 ONE MARK

Q. 11 Choose the most appropriate alternative from the options given below to completethe following sentence :

Suresh’s dog is the one ........................was hurt in the stampede.(A) that (B) which

(C) who (D) whom

Q. 12 The cost function for a product in a firm is given by ,q 5 2 where q is the amount

of production. The firm can sell the product at a market price of Rs. 50 per unit.The number of units to be produced by the firm such that the profit maximized is(A) 5 (B) 10

(C) 15 (D) 25

Q. 13 Choose the most appropriate alternative from the options given below to completethe following sentence.Despite several ..................the mission succeeded in its attempt to resolve the

conflict.

(A) attempts (B) setbacks

(C) meetings (D) delegations

Q. 14 Which one of the following options is the closest in meaning to the word given

below ?Mitigate(A) Diminish (B) Divulge

(C) Dedicate (D) Denote

Q. 15 Choose the grammatically INCORRECT sentence :

(A) They gave us the money back less the service charges of Three HundredRupees.

(B) This country’s expenditure is not less than that of Bangladesh.

(C) The committee initially asked for a funding of Fifty Lakh rupees, but latersettled for a lesser sum.

(D) This country’s expenditure on educational reforms is very less.







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YEAR 2012 TWO MARKS

Q. 16 Given the sequence of terms, AD CG FK JP , the next term is(A) OV (B) OW

(C) PV (D) PW

Q. 17 Wanted Temporary, Part-time persons for the post of Field Interviewer to

conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work.Transportation paid, expenses reimbursed.Which one of the following is the best inference from the above advertisement

?(A) Gender-discriminatory

(B) Xenophobic

(C) Not designed to make the post attractive

(D)Not gender-discriminatory

Q. 18 A political party order an arch for the entrance to the ground in which theannual convention is being held. The profile of the arch follows the equations

.y x x 2 0 1 2

= − where y is the height of the arch in meters. The maximum possibleheight of the arch is

(A) 8 meters

(B) 10 meters

(C) 12 meters

(D) 14 meters

Q. 19 An automobile plant contracted to buy shock absorbers from two suppliers X and Y . X supplies 60% and Y supplies 40% of the shock absorbers. All shockabsorbers are subjected to a quality test. The ones that pass the quality testare considered reliable. Of X ’s shock absorbers, 96% are reliable. Of Y ’s shock

absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to bereliable, is made by Y is(A) 0.288

(B) 0.334

(C) 0.667

(D) 0.720

Q. 20 Which of the following assertions are CORRECT ?

P : Adding 7 to each entry in a list adds 7 to the mean of the listQ : Adding 7 to each entry in a list adds 7 to the standard deviation of the

list

R : Doubling each entry in a list doubles the mean of the list

S : Doubling each entry in a list leaves the standard deviation of the list







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unchanged

(A) ,P Q (B) ,Q R

(C) ,P R (D) ,R S

YEAR 2011 ONE MARK

Q. 21 Choose the word from the options given below that is most nearly opposite inmeaning to the given word :

Amalgamate(A) merge (B) split

(C) collect (D) separate

Q. 22 Which of the following options is the closest in the meaning to the word below :

Inexplicable(A) Incomprehensible (B) Indelible

(C) Inextricable (D) Infallible

Q. 23 If / /log log logP Q R1 2 1 3= =^ ^ ^ ^ ^h h h h h, then which of the following options is

TRUE ?(A) P Q R2 3 2

= (B) Q PR2=

(C) Q R P 2 3= (D) R P Q 2 2

=

Q. 24 Choose the most appropriate word from the options given below to complete the

following sentence.In contemplated................Singapore for my vacation but decided against it.(A) to visit (B) having to visit

(C) visiting (D) for a visit

Q. 25 Choose the most appropriate word from the options given below to complete thefollowing sentence.

If you are trying to make a strong impression on your audience, you cannot doso by being understated, tentative or(A) hyperbolic (B) restrained

(C) argumentative (D) indifferent

YEAR 2011 TWO MARKS

Q. 26 A container originally contains 10 litres of pure spirit. From this container 1 litreof spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture isagain replaced with 1 litre of water and this processes is repeated one more time.How much spirit is now left in the container ?

(A) 7.58 litres (B) 7.84 litres

(C) 7 litres (D) 7.29 litres

Q. 27 Few school curricula include a unit on how to deal with bereavement and grief,and yet all students at some point in their lives suffer from losses through deathand parting.Based on the above passage which topic would not be included in a unit onbereavement ?(A) how to write a letter of condolence







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(B) what emotional stages are passed through in the healing process

(C) what the leading causes of death are

(D) how to give support to a grieving friend

Q. 28 The variable cost (V ) of manufacturing a product varies according to the equation4V q = , where q is the quantity produced. The fixed cost F ^ h of production of

same product reduces with q according to the equation /F q 100= . How manyunits should be produced to minimize the total cost V F +^ h ?(A) 5 (B) 4

(C) 7 (D) 6

Q. 29 P , Q , R and S are four types of dangerous microbes recently found in a human

habitat. The area of each circle with its diameter printed in brackets representsthe growth of a single microbe surviving human immunity system within 24 hours

of entering the body. The danger to human beings varies proportionately with thetoxicity, potency and growth attributed to a microbe shown in the figure below :

A pharmaceutical company is contemplating the development of a vaccine against

the most dangerous microbe. Which microbe should the company target in itsfirst attempt ?(A) P (B) Q

(C) R (D) S

Q. 30 A transporter receives the same number of orders each day. Currently, he has

some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the endof the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks,

then all the orders are cleared at the end of the 10th day. What is the minimumnumber of trucks required so that there will be no pending order at the end ofthe 5th day ?(A) 4 (B) 5

(C) 6 (D) 7

2010 ONE MARK

Q. 31 Which of the following options is the closest in meaning to the word below ?Circuitous

(A) Cyclic (B) Indirect

(C) Confusing (D) Crooked

Q. 32 The question below consist of a pair of related words followed by four pairs of







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words. Select the pair that best expresses the relation in the original pair.

Unemployed : Worker(A) Fallow : Land (B) Unaware : Sleeper

(C) Wit : Jester (D) Renovated : House

Q. 33 Choose the most appropriate word from the options given below to complete the

following sentence :If we manage to ........ our natural resources, we would leave a better planet forour children.(A) unhold (B) restrain

(C) cherish (D) conserve

Q. 34 Choose the most appropriate word from the options given below to complete thefollowing sentence :

His rather casual remarks on politics..................his lack of seriousness about thesubject.(A) masked (B) belied

(C) betrayed (D) suppressed

Q. 35 25 persons are in a room 15 of them play hockey, 17 of them play football and10 of them play hockey and football. Then the number of persons playing neitherhockey nor football is

(A) 2 (B) 17

(C) 13 (D) 3

2010 TWO MARKS

Q. 36 Modern warfare has changed from large scale clashes of armies to suppression ofcivilian populations. Chemical agents that do their work silently appear to be

suited to such warfare ; and regretfully, their exist people in military establishmentswho think that chemical agents are useful fools for their cause.Which of the following statements best sums up the meaning of the above passage?

(A) Modern warfare has resulted in civil strife.

(B) Chemical agents are useful in modern warfare.

(C) Use of chemical agents in ware fare would be undesirable.

(D) People in military establishments like to use chemical agents in war.

Q. 37 If 137 276 435+ = how much is 731 672+ ?

(A) 534 (B) 1403

(C) 1623 (D) 1531

Q. 38 5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a

wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build thewall ?(A) 20 days (B) 18 days

(C) 16 days (D) 15 days







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Q. 39 Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how much distinct 4 digit numbers greater than

3000 can be formed ?(A) 50 (B) 51

(C) 52 (D) 54

Q. 40 Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters.)

All were born on 1st January. The age difference between any two successivesiblings (that is born one after another) is less than 3 years. Given the followingfacts :1. Hari’s age + Gita’s age > Irfan’s age + Saira’s age.

2. The age difference between Gita and Saira is 1 year. However, Gita is notthe oldest and Saira is not the youngest.

3. There are no twins.

In what order were they born (oldest first) ?(A) HSIG (B) SGHI

(C) IGSH (D) IHSG

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SOLUTION

Sol. 1 Option (C) is correct.

Option (C) is grammatically incorrect because ‘European’ pronunciate with

consonent sound although starts with vowel ‘E’. Therefore the article ‘a’ should

be used instead of ‘an’.


Series may be written as .......0 2 4 44+ + + +

In A.P. the number of term n th a n d 1= + −^ hwhere a =1st term in series 0=

n th termn 44th

= =

d difference 2= =

So that n th a n d 1= + −^ h 44 0 n 1 2= + −^ ^h hor n 23=

And the sum of these numbers in .A P

sum

n a n d

2 2 1

= + −^ h6 @

2

232 0 23 1 2# #= + −^ h6 @

2

2344 23 22 506# #= = =

Sol. 3 Option (A) is correct.

This is a conditional sentence, in which if sentence starts with ‘were’ or ‘should’

then the second part of the sentence after comma. uses ‘would + Ist form of

verbs’.

Sol. 4 Option (B) is correct.

Nadir – means the lowest point in the fortunes of a person or organization.Sol. 5 Option (A) is correct.

‘Particularism’ is the opposite of Universalism’ Therefore the opposite of

diffuseness is ‘specificity’.


(i) Since labour wages per day increase by 15 of the current wages. Hence new

labour wages per day

15

1= +

5

6= per day

(ii) The working hours decrease by 124 of the current period. Hence new

working period 1

24

1

24

23= − =

Therefore the commulative factor which affect the current erection cost ofstructure due to above condition is

1. 5 times5

6

24

231#= =







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Now, the new cost of erection

1. 5 132001 #=

.15180Rs

=

Sol. 7 Option (D) is correct.

In given paragraph, spider makes repeated efforts even after failure. It means

spider did not give up hope after adversity of failure. Hence assertion ‘No adversity

justifies giving up hope” is best supported by the above information.


Let total distance travelled kmd =

Distance d 2

travelled with 60 /km h

So the time taken to travel /d 2 distance is

t 1 hours

d d 2 60 120#= =

Distance d 4 travelled with 30 /km h


t 2 hoursd d

4 30 120#= =

and rest of distance d 4^ h is travelled with 10 /km h


t 3 d d

4 10 40#= = hour

Total time of journey

d d d d d 120 120 40 120

5

24= + + = = hours

Total distance travelled kmd =

Therefore average speed of journey

24 24 /km hd d

#= =


Given Series is

...........................1 2

1

2 3

1

3 4

1

80 81

1

++

++

++ +

+

By multiplying and dividing each term of series with their opposite sign

denominator, we have

1 2

1

2 1

2 1

2 3

1

3 2

3 2# #=

+ −

−+

+ −

−+^ ^h h

...........80 81

1

81 80

81 80#+

+ −

−

or .............2 1

2 1

3 2

3 2

81 80

81 80=

−

−+

−

−+

−

−

.........

1

2 1 3 2 4 3 81 80=

− + − + − + −

or1

81 1- 9 1 8= − =

Sol. 10 Option (D) is correct.There are total 90, 2-digit integers between 1 and 100.

Therefore Total condition for this sample n 90=

Out of there conditions, there are only 13 condition which are divisible by 7.

Hence the total favorable condition which are not divisible by 7 are







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n 13- 90 13 77= − =

Therefore the probability that the selected number is not divisible by 7 is

Total conditions

conditions which are not divisible by 7

n

=

^ h

90

77=


“Which” is used in a sentence when the person is unknown. But here the person

means Suresh’s dog is known and “that” is used in a sentence, when the person

is known.

So, that will be used in this sentence.


Profit is given by,

P cosSelling price Total t of production= −

q q 50 5 2

= −

Using the principle of max minima ima- ,

dq dP q 50 10 0= − =

q 10

505= =

anddq

d P 2

2

10=− (maxima)

So, for 5 units the profit is maximum.


Despite several setbacks the mission succeeded in its attempt to resolve the

conflict.


From the following options Diminish is the closest meaning to the Mitigate.


The grammatically incorrect sentence is :

(A) They gave us the money back less the service charges of three hundred rupees.


So, the next term is OV .


Not gender-discriminatory

Discriminatory involves the actual behaviors towards groups such as excluding or

restricting members of one group from opportunities that are available to another

group.

This given advertisement is not exclude or restrict Male or Female members fromone another. Hence this is Not-gender discriminatory.


We have y .x x 2 0 1 2

= − ...(i)

Using the principle of max minima ima- ,







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dx dy

. x 2 0 2 0= − =

x .0 2

210= =

Anddx

d y 2

2

.0 2=− (maxima)

So, for maximum possible height, substitute x 10= in equation (i),

y . ( )2 10 0 1 10 2# #= −

20 10 10 meter= − =


Supplier X supplies 60% of shock absorbers, out of which 96% are reliable. So

overall reliable fraction of shock absorbers from supplier X ,

. .0 6 0 96#=

.0 576=

And for supplier Y , suppliers 40% of shock absorbers, out of which 72% are

reliable. So fraction of reliability . . .0 4 0 72 0 288#= = .

Total fraction of reliability . . .0 576 0 288 0 864= + =

Hence the probability that is found to be reliable, is made by Y is,

. .

..

0 288 0 576

0 2880 334=

+ =


For statement P , take three variables , ,a b c

Mean ( )m a b c 3= + +

Adding 7 to each entry,

m 1 ( ) ( ) ( )a b c

37 7 7

=+ + + +

m 1 a b c

m 3 3

217=

+ ++ = +

So, it is correct.

( )Q Standard deviation

s ( ) ( ) ( )a m b m c m

3

2 2 2

=− + − + −

Adding 7 to each entry, 1s ( ) ( ) ( ) ( )a m b m c m 7 7 7 72 2 2

! s = − + + − + + − + +

It is wrong.

( )R By doubling each entry.

m 1 a b c

m 3

2 2 22=

+ += (it is correct)

( )S doubling each entry

1s ( ) ( ) ( )

(2 )m a m b m c

32 2 22 2 2

! s =− + − + −

Hence it is wrong.Sol. 21 Option (B) is correct.

Amalgamate means combine into a unified or integrated whole unit. The word

split is nearly opposite in meaning to the Amalgamate.







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Inexplicable means incapable of being explained or accounted. So, the best

synonym here is incomprehensible.

Sol. 23 Option (B) is correct.We have

log P ^ h log logQ R21

31

= =^ ^h hor log P ^ h log log logQ R C / /1 2 1 3

= = =^ ^h hWhere logC is a constant.

or P C = , Q C 2= , R C 3

=

Now From option (ii),

Q 2 PR=

C 2 2^ h C C 3#=

C 4 C 4=

Equation (ii) satisfies.


The correct usage of contemplate is verb + ing form. It is a transitive verb. The

most appropriate work is visiting.


The mean of the sentence indicates a word that is similar to understand is needed

for the blank place.

Therefore, the best option is restrained which means controlled or reserved.Sol. 26 Option (D) is correct.

We know

Quantity of spirit left after n th operation a a

a b n

#=−b l

Where a = initial quantity of pure spirit

and b = quantity taken out and replaced every time

Now after three n 3=^ h operations,

Left quantity of spirit after 3rd operation

10 10

10 1

10 10

93 3

=−

=

b bl l 7.29 litre=


This passage deals with how to deal with bereavement and grief. So, after the

tragedy occurs and it is not about precautions. Thus option (C), what the

leading causes of death are, not be included in a unit of bereavement. Rest all are

important in dealing with grief.


Total cost = Variable cost + Fixed Cost

. .T C V F = +

q q 4 100= +

Not for minimize the total cost, using the options.

(A) For q 5= , . .T C 4 55

10040#= + =

(B) For q 4= , . .T C 4 44

10041#= + =







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(C) For q 7= , . .T C .4 77

10042 28#= + =

(D) For q 6= , . .T C 4 6 40.666

100#= + =

Hence, option (A) gives the minimum cost.


The danger of a microbe to human being will be directly proportional to potency

and growth and inversely proportional to the toxicity.

So, level of dangerousToxicity

Potency growth\

#

D C T

PG = Where C = constant of proportionality

For P , D P . .800

0 4 25 0 98

2

# #p= =^ h

For Q , D Q .

.600

0 5 201 047

2

# #p

= =^ h

For R, D R .

.300

0 4 150 94

2

# #p

= =^ h

For S , D S .

.200

0 8 101 25

2

# #p

= =^ h

Thus D S is maximum and it is most dangerous among them and it is targeted in

first attempt.


Let ‘x ’ be the number of orders each day and y be the backlogs.

So, From the given conditions

x y 4 + 4 7 28#= =

and x y 10 + 3 10 30#= =

After solving these two equations, we get

x 3

1= , y

3

80=

Now determine the number of trucks, so that no pending order will be left end of

the 5th day. x y 5 + n 5=

Where n = Number of trucks

n .5

53

1

3

80

5

3

85

5 56#

=

+

= =

Hence number of trucks have to be natural number,

n 6=


Circuitous means round about or not direct. Indirect is closest in meaning to this

circuitous(A) Cyclic : Recurring in nature

(B) Indirect : Not direct

(C) Confusing : lacking clarity of meaning

(D) Crooked : set at an angle; not straight







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A worker may by unemployed. Like in same relation a sleeper may be unaware.


Here conserve is most appropriate word.


Betrayed means reveal unintentionally that is most appropriate.


Number of people who play hockey ( )n A 15=

Number of people who play football ( )n B 17=

Persons who play both hockey and football ( )n A B + 10=

Persons who play either hockey or football or both :

( )n A B ,

( ) ( ) ( )n A n B n A B += + −

15 17 10 22= + − =

Thus people who play neither hockey nor football 25 22 3= − =



Since 7 6 13+ = but unit digit is 5 so base may be 8 as 5 is the remainder when

13 is divided by 8. Let us check.

137

276

435

8

8

731

672

1623

8

8

Thus here base is 8. Now

Sol. 38 Option (D) is correct.Let W be the total work.

Per day work of 5 skilled workers W 20

=

Per day work of one skill worker W W 5 20 100#

= =

Similarly per day work of 1 semi-skilled workersW W

8 25 200#= =

Similarly per day work of one semi-skill worker W W 10 30 300#

= =

Thus total per day work of 2 skilled, 6 semi-skilled and 5 unskilled workers is

2 6 5 12 18 10W W W W W W W 100 200 300 600 15= + + = + + =

Therefore time to complete the work is 15 days.


As the number must be greater than 3000, it must be start with 3 or 4. Thus we

have two case:

Case (1) If left most digit is 3 an other three digits are any of 2, 2, 3, 3, 4, 4, 4, 4.

(1) Using 2, 2, 3 we have 3223, 3232, 3322 i.e.!

!3

2

3= no.

(2) Using 2,2,4 we have 3224, 3242, 3422 i.e.!

!3

2

3= no.

(3) Using 2,3,3 we have 233, 323, 3323 3 3 i.e.!

!3

2

3= no.

(4) Using 2,3,4 we have !3 6= no.

(5) Using 2,4,4 we have 244, 424, 4423 3 3 i.e.!

!3

2

3= no.







(6) Using 3,3,4 we have 334, 343, 4333 3 3 i.e.!

!3

2

3= no.

(7) Using 3,4,4 we have 344, 434, 4433 3 3 i.e.!

!3

2

3= no.

(8) Using 4,4,4 we have 3444 i.e.!

!

3

31= no.

Total 4 digit numbers in this case is

1 3 3 3 6 3 3 3 1 25+ + + + + + + + =

Case 2 : If left most is 4 and other three digits are any of 2, 2, 3, 3, 3, 4, 4, 4.

(1) Using 2,2,3 we have 4223, 4232, 4322 i.e. .!

!3

2

3= no

(2) Using 2,2,4 we have 4224, 4242, 4422 i.e. .!

!3

2

3= no

(3) Using 2,3,3 we have 4233, 4323, 4332 i.e. . !

!

32

3= no

(4) Using 2,3,4 we have i.e. . !3 6= no

(5) Using 2,4,4 we have 4244, 4424, 4442 i.e. .!

!3

2

3= no

(6) Using 3,3,3 we have 4333 i.e!

!

3

31= . no.

(7) Using 3,3,4 we have 4334, 4343, 4433 i.e. .!

!3

2

3= no

(8) Using 3,4,4 we have 4344, 4434, 4443 i.e. .!

!3

2

3= no

(9) Using 4,4,4 we have 4444 i.e.!!

33 1= . no

Total 4 digit numbers in 2nd case 3 3 3 6 3 3 1 3 1 26= + + + + + + + + =

Thus total 4 digit numbers using case (1) and case (2) is 25 26 51= + =


Let H , G , S and I be ages of Hari, Gita, Saira and Irfan respectively.

Now from statement (1) we have H G > I S + +

Form statement (2) we get that G S 1− = or S G 1− =

As G can’t be oldest and S can’t be youngest thus either GS or SG possible.

From statement (3) we get that there are no twins(A) HSIG : There is I between S and G which is not possible

(B) SGHI : SG order is also here and S > G > H > I G H > S I and + + whichis possible.

(C) IGSH : This gives I G > and S H > and adding these both inequalities wehave I S H G >+ + which is not possible.

(D) IHSG : This gives I H > and S G > and adding these both inequalities we

have I S H G >+ + which is not possible.

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