number system Model Questions & Answers, Practice Test for ibps clerk prelims

Answer: (c)

Given that n is greater then 1, then $n^2 (n^2 – 1)$ is always divisible by 12.

Example 1: Put n = 2, then

$n^2 (n^2 – 1) = (2)^2 (2^2 – 1)$

= 4 × 3 = 12.

Hence $n^2 (n^2 – 1)$ is divisible by 12 but not by 24, 48 and 60 for n = 2.

Answer: (c)

Let two digits of the number are x and y, then

xy = 8 ⇒ y = 8/x ...(i)

(10x + y) = 4 (10y + x) + 9

10x + y = 40y + 4x + 9

6x = 39y + 9

2x = 13y + 3

$2x = 104/x + 3$ $(∵ y = 8/x)$

$2x^2 – 3x – 104 = 0$

⇒ x = 8, $13/2$

∴ x = 8, y = 1

Required number = 81

Answer: (d)

$12^55/3^11 = 3^44.{4}^55$ → 4 as units place.

Similarly, $8^48/16^18 = 2^72$ → 6 as the units place.

Hence, 0 is the answer.

Answer: (d)

234 × 167 = 39078

Answer: (c)

Total numbers in the set = (800 – 200) + 1 = 601

Number of numbers which are divisible by 5

= $(800 - 200)/5 + 1 = 121$

Number of numbers which are divisible by 7

= $(798 - 203)/7 + 1= 86$

Number of numbers which are divisible by both 5 & 7

= $(770 - 210)/35 + 1 = 17$

∴ Number of numbers which are either divisible by 5 or 7 or both

= (121 + 86) – 17 = 190