100+ Number System Questions for UPSC Exams - 1

Ans: A

(6 + 12 + 18 + 24 + ….. + 60)
= 6 x (1 + 2 + 3 + 4 + ….+ 10) = 6 × 55 = 330.

Ans: B

Sum of the digits in respective number is 9, 12, 18, 9, 21, 12, 18, 21, 15 and 24.

Out of these 12, 21, 12, 21, 15, 24 are divisible by 3 but not by 9.

So, the number of required numbers is 6.

Ans: A

Unit digit in the given product = 8.

Unit digit of (9 × 6 × x × 4) is 8. So, x = 3.

Ans: B

a. In 183654729, 1836547 is not divisible by 7.

b. In 381654782, 38 is divisible by 2, 381 is divisible by 3, 3816 is divisible by 4, 38165 is divisible by 5, 381654 is divisible by 6, 3816547 is divisible by 7, 38165472 is divisible by 8 and 381654729 is divisible by 3.

c. In 983654721, 983 is not divisible by 3.

d. In 981654723, 9816547 is not divisible by 7.

Ans: D

Let 3578 + 5729 – x × 581 = 5821. Then

x × 581 = (3578 + 5729) - 5821

⇒ x × 581 = (9307 - 5821)

= 3486 ⇒ x = $${3486}/{581}$$ = 6.