Prepscholar Interview Questions, Process, and Tips

LET ACTUAL PRICE BE 100 RS(FOR CONVINIENCE)
THEREFORE IF PRICE IS CUT BY 20%
THEREFORE NEW PRICE=100-20=80 RS
THEREFORE WE NEED TO ADD X% TO 80 RS TO MAKE IT 20 RS AND ADD IT TO 80 TO MAKE IT 100RS
THEREFORE, 80X/100 = 20
I.E. 4X/5=20
THEREFORE x=20*5/4
=5*5
=25
HENCE 25% OF PRICE SHOULD BE ADDED TO MAKE THE PRICE EQUAL TO THE ACTUAL PRICE.

360

slower train – 48 kmph = 40/3 m/s
say faster train, v m/s
therefore, {v-(40/3)}*180 = 600, => v= 60 kmph

10000

one-legged =5% of 10000=500

remaining=10000-500=9500

barefooted=9500/2=4750

remaining people= 9500-4750=4750

hence required number of shoes= 4750*2+500*1=100005% of 10000 = 500 one legged

9500 / 2 = 4750 bare foot

minium no of shoes = 4750*2 + 500*1 = 10000

C

C

To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.

The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.

There are 24 primes in S, so the product of S is:

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97

We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.

5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.

25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.

Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros

C

625

If Vijay gives ‘x’ marbles to Ajay then Vijay and Ajay would have V – x and A + x marbles.
V – x = A + x — (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A – 2x and V + 2x marbles.
V + 2x – (A – 2x) = 30 => V – A + 4x = 30 — (2)
From (1) we have V – A = 2x
Substituting V – A = 2x in (2)
6x = 30 => x = 5.