number system Model Questions & Answers, Practice Test for ssc cgl tier 2

Answer: (a)

The number needs to be less than 13 × 52 = 676.

The highest power of 13 in 676! is 56.

The power of 13 in the smallest such number needs to be exactly 52.

If we subtract 13 × 3 = 39 from 676, we get 637.

The number 637! will be the smallest number of type N! that is completely divisible by 1352.

The sum of the digits of 637 is 16.

Answer: (d)

The largest integer that divides product of any four consecutive integers is 4!

i.e., 24. e.g., 1, 2, 3, 4 are four consecutive integers.

Multiplication = 1 × 2 × 3 × 4 = 24 which is divided by 24.

Answer: (a)

Statement 1

= 111 (X + Y + Z), which is divisible by (X + Y + Z)

So, it is not correct

Statement 2

= 111 (X + Y + Z), which is divisible by 111

So, it is correct

Answer: (c)

Unit digit in $7^4$ is 1.

So, unit digit in $7^92$ is 1.

∴ Unit digit in $7^95$ is 3.

Unit digit in $3^4$ is 1.

∴ Unit digit in $3^56$ is 1.

∴ Unit digit in $3^58$ is 9.

∴ Unit digit in $(7^95 – 3^58)$

= (13 – 9) = 4.

Answer: (b)

Let two digit number = 10y + x

According to question,

Ist condition, 10y + x = k(x + y) ...(1)

2nd condition, 10x + y = m(x + y) ...(2)

Adding (1) and (2) we get

11x + 11y = (k + m) × (x + y)

11(x + y) = (k + m) (x + y)

k + m = 11 ⇒ m = 11 – k

∴ Option (c) is correct