Showcase publications Interview Questions, Process, and Tips

119

=36*84/ lcm
= 36 * 84 / (12 * 3 * 7 )
HCF= 12

Yes answer is 18 days

13km

The first number is 10 and the second number is 5

2380

D

38 years

Let Rajan’s present age be x years. Then, his age at the time of marriage = (x – 8) years.

x = 65(x−8)

⇒5x=6x−48

⇒x=48 years

Rajan’s sister’s age at the time of his marriage = (x – 8) – 10 = (x – 18) = 30 years

∴ Rajan’s sister’s present age = (30 + 8) years = 38 years

Because he is very short for his height he can press upto 18th floor button only

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

Hard work would mean spending long hours to complete my work without any shortcuts. It definitely ensures results but the process is long and stressful. Smart work would be aiming for the same results but with planning and prioritization of tasks.

42m

Relative speed =65-45km/hr
Relative speed=20km/hr
Convert to m/s
S=20*5/18
S=5.555
Length of the faster train =5.55555*18seconds
=100meters