number system Model Questions & Answers, Practice Test for ssc cgl tier 1 2024

Answer: (a)

Since the given number is divisible by 5, so 0 or 5 must come in place of #.

But, a number ending with 5 is never divisible by 8.

So, 0 will replace #.

Now, the number formed by the last three digits is 4*0, which becomes divisible by 8, if * is replaced by 4.

Hence, digits in place of * and # are 4 and 0 respectively.

Answer: (a)

$1/m + 4/n = 1/12$

⇒ 12n + 48m – mn – 576 = – 576

$m - 12 = 576/{n - 48}$ ...(i)

Since n is an odd, therefore, (n – 48) is an odd.

Also – 576 is an even, therefore (m – 12) is definitely even.

Now n is an odd integer less than 60.

Hence, on checking, we get all possible value of n are 49, 51 and 57.

Therefore, there are three value of n

Answer: (d)

786 × 964 = 757704.

Answer: (d)

Given a = 6b = 12c = 27d = 36e

Multiplied and Divide by 108 in whole expression

${108a}/108 = {108b}/18 = {108c}/9 = {108d}/4 = {108e}/3$

$1/108a = 1/18b = 1/9c = 1/4d = 1/3e = 1$(say)

⇒ a = 108, b = 18, c = 9, d = 4, e = 3

So it is clear that , $(a/6, c/d)$ contains a number $c/d = (9/4)$ which is not an integer

Answer: (c)

When $2^256$ is divided by 17 then

⇒ $2^256/{2^4 + 1} ⇒ (2^2)^64/(2^4 + 1)$

By remainder theorem when f(x) is divided by x + a the remainder = f(– a)

Here f(1) = $(2^2)^64$ and x = $2^4$ and a = 1

∴ Remainder = f (–1) = $(–1)^64$ = 1