# eLitmus Previous year paper 1

SECTION 1 : QUANTITATIVE APTITUDE

Let A be a natural number consisting only 1. B is another natural number which is equal to quotient when A is divided by 13. C is yet another natural number equal to the quotient when B is divided by 7. Find B-C.
A.     7236
B.     7362
C.     7326
D.     None of these

A biker notices a certain number(2 digits number) on the milestone before starting the journey. After riding for an hour he notices a milestone with reversed digits of the previous number. Now after riding for another hour he notices that the number on a new milestone had same digits as the first one (in the same order) but with a "0" between the 2 digits. If the rider maintains a constant speed throughout, Calculate his speed.
A.     45 kmph
B.     50 kmph
C.     35 kmph
D.     None of these

PT Usha and Shelly John decide to run a marathon between Ramnagar and Jamnagar. Both start from Ramnagar at 1 pm. On the way are two towns Ramgarh and Rampur, separated by a distance of 15 km. PT Usha reaches Ramgarh in 90 minutes running at a constant speed of 40 kmph. She takes additional 30 minutes to reach Rampur. Between Rampur and Jamnagar she maintains an average speed of V kmph (where V is a whole number),Shelly John being a professional marathon runner, maintains a constant speed of 18 kmph. They both reach Jamnagar together after ‘n’ hours, ‘n’ being a whole number. What could be total time taken by PT Usha?
A.     5 hours
B.     15 hours
C.     41 hours
D.     All of the above

/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a + b ) ( b + c ) ( c + a )?
A.     Equal to 0
B.     Greater than 0
C.     Less than 0
D.     Cannot be determined

Find the number of ways you can fill a 3 x 3 grid (with 4 corners defined as a, b, c, d), if you have 3 white marbles and 6 black marbles.
A.     75
B.     84
C.     80
D.     None of these
Explanation :
The area of the grid is = 9.
Now, No. of ways we can arrange 3 white balls in 9 places = 9c3.
and 6 black balls in (9-3) = 6 places = 6c6 = 1.
So total = 9c3 * 1 = 9c3 = 9 * 8 * 7/3 * 2 *1 = 84.

How many 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place?
A.     120
B.     100
C.     130
D.     90

if log xy2 =a, log x3y =b,find log y/log x = ?
A.     3a-b/2b-a
B.     3a-b/2b+a
C.     3a+b/2b-a
D.     3a-b/2b

What is the difference between highest ever increasing number and second highest ever increasing number? (eg. 19,12345,189..etc)
A.     1
B.     10
C.     100000
D.     1,111,11,111

Maximum value of N for {(1008)-(1111122)} is divisible by 3N. What will be maximum value for N?
A.     6
B.     2
C.     1
D.     0

In a party men drink only beer,women drink only wine,sons drink only orange juice & daughters drink only apple juice.There are 1.05L of beers, 1.05L of wine 3.5L of orange juice and 4.9L of apple juice. If every one has the same drinking capacity then what can be the minimum number of people present at the party?
A.     30
B.     32
C.     35
D.     None of these

In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?
A.     0
B.     12
C.     13
D.     20

A report has 20 sheets each of 55 lines and each line consists of 65 characters. If this report is to be retyped with each sheet having 65 lines and each line of 75 characters what will be the reduction percent in the pages ?
A.     22.5 %
B.     35 %
C.     25 %
D.     None of these

The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800 ?
A.     16
B.     24
C.     20
D.     18
E.     22

The bankers discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
A.     Rs. 360
B.     Rs. 432
C.     Rs. 540
D.     Rs. 1080

Find the probability that the sum of n numbers is divisible by n ,,assuming n is very large no.
A.     1
B.     1/2
C.     3/4
D.     None of these
E.     Can't be determined.

For two positive integers a and b define the function h(a,b) as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the G.C.F of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is
A. n/2
B. n-1
C. n
D. None of these

How many three digit number satisfies the following condition ?

a) When dividd by 11 or 12 leave remainder 7& 8 Respectively.

b) When divided by 33 or 24 lweave remiander 29 & 20 resp.

c) When divided by 7 or 8 leave remainder 4 in each case.

A.     5
B.     3
C.     1
D.     None of these

Let n! = 1 x 2 x 3 ........n for integer n ≥ 1. If p = 1! + (2 x 2!) + + (3 x 3!) + .......+ (10 x 10!), then p + 2 when divided by 11! leaves a remainder of
A.     10
B.     0
C.     7
D.     1

What is the remainder when N= (1! +2! +3! +4! +... + 1000!)40 is divided by 10?
A.     1
B.     2
C.     3
D.     7

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square. The proportion of the sheet area that remains after punching is :-
A.     (π + 2)/8
B.     (6 - π)/8
C.     (4 - π)/4
D.     (π - 2)/4
E.     (14 - 3π)/6

Find the values of n for which n+18 and n+90 is a perfect square ?
A.     6
B.     5
C.     4
D.     3

If | r- 6 | = 11 and |2q - 12| = 8, what is the minimum possible value of q / r ?
A.     -2/5
B.     -2
C.     10/17
D.     None of these

If a1 = 1 and an+1 = 2an + 5, n=1, 2....... then a100 is equal to
A.     5 x 2^99 - 6
B.     5 x 2^99 + 6
C.     6 x 2^99 + 5
D.     6 x 2^99 - 5Let R1 and R2 respectively denote the maximum and minimum possible

remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.
A.     90
B.     82
C.     84
D.     64

If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?
A.     3/2
B.     sqrt(15)
C.     sqrt(6)/2
D.     15

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SECTION 2 : LOGICAL REASONING

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SECTION 3 : VERBAL ABILITY [ENGLISH]

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