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

Answer: (a)

Every prime number of the form 3k + 1 can be represented in the form 6m + 1 only, when k is even.

Answer: (d)

By considering every option

(a) 3q + 9 = 18 ⇒ q = 3

Then, numbers are 3, 5 and 9, which are not all prime.

(b) 3q + 9 = 42 ⇒ q = 11

Then, numbers are 11, 13, 17, which are all prime

(c) 3q + 9 = 60 ⇒ q = 17

Then, numbers are 17, 19 and 23 which are all prime.

Hence, option (d) is correct.

Answer: (d)

Required product = 768 × 859 = 659712

Answer: (c)

Required amount = $41910/22$ = Rs. 1905

Answer: (c)

Remember that, $a^3 + b^3 = (a + b) (a^2 + b^2 – ab)$

$x = (16^3 + 17^3 + 18^3 + 19^3)$

$x = (16^3 + 19^3) + (17^3 + 18^3)$

$x = (16 + 19) (16^2 + 19^2 – 16 × 19) + (17 + 18) (17^2 + 18^2 – 17 × 18)$

$x = 35[16^2 + 19^2 – 16 × 19 + 17^2 + 18^2 – 17 × 18]$

x = 35 × (Even number)

Hence, x is divisible by 70 and leaves remainder as zero.