number system Model Questions & Answers, Practice Test for ssc chsl tier 1 2023

Question :21

When 96 is added to a $N^2$ , it gives another perfect square. If N is a natural no., how many distinct values of N are possible?

Answer: (b)

$N^2 + 96 = P^2$ , or, 96 = $P^2 – N^2$.

Now factorize 96 and equate it with (P + N) (P – N).

Question :22

If 653xy is divisible by 80 then the value of x + y is

Answer: (d)

Since 80 = 8 × 10 or 80 = 16 × 5

Thus y (i.e., unit digit) must be zero.

∴ 653xy = 653x0, where 653x0 must be divisible by 16 or 653x is divisible by 8.

Thus the last 3-digit number 53x will be divisible by 8.

Hence, at x = 6, we get the required result.

∴ x + y = 6 + 0 = 6

Question :23

Two numbers when divided by a certain divisor leave the remainders 4375 and 2986 respectively; but when the sum of the two numbers be divided by the same divisor, the remainder is 2361. The divisor is

Answer: (c)

Required Divisor = (sum of remainders)

– Remainder when sum is divided

= [ 4375 + 2986] – 2361 = 5000

Question :24

The sum of prime numbers that are greater than 60, but less than 70 is

Answer: (c)

Sum of prime numbers that are greater than 60, but less than 70 is

61 + 67 = 128

Question :25

What is 234 times 167 ?

Answer: (d)

234 × 167 = 39078

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