Number System - Study Mode

[#546] Which of the following number is divisible by 24 ?
Correct Answer

(D) 3125736

Explanation

Solution: 24 = 3 × 8, where 3 and 8 co-prime Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8 Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8 Consider option (D), Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3 Also, 736 is divisible by 8 ∴ 3125736 is divisible by (3 × 8), i.e., 24

[#547] On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
Correct Answer

(D) 4

Explanation

Solution: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder ∴ x = 5k + 3 ⇒ x 2 = (5k + 3) 2 ⇒ x 2 = (25k 2 + 30k + 9) ⇒ x 2 = 5 (5k 2 + 6k + 1) + 4 ∴ On dividing x 2 by 5, we get 4 as remainder

[#548] On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
Correct Answer

(C) 5

Explanation

Solution: Let x be the number and y be the quotient. Then, x = 357 × y + 39 = (17 × 21 × y) + (17 × 2) + 5 = 17 × (21y + 2) + 5 ∴ Required remainder = 5

[#549] Arrangement of the fractions into ascending order : $$frac{4}{3},$$ $$ - frac{2}{9},$$ $$ - frac{7}{8},$$ $$frac{5}{{12}}$$
Correct Answer

(B) $$ - frac{7}{8}, - frac{2}{9},frac{5}{{12}}frac{4}{3}$$

Explanation

Solution: $$frac{4}{3}, - frac{2}{9}, - frac{7}{8},frac{5}{{12}}$$ $$eqalign{
& frac{4}{3} = 1.33, cr
& - frac{2}{9} = - 0.22, cr
& - frac{7}{8} = - 0.875, cr
& frac{5}{{12}} = 0.416 cr} $$ So, $$ - frac{7}{8}, - frac{2}{9},frac{5}{{12}},frac{4}{3}$$

[#550] If 1 3 + 2 3 + .....+ 10 3 = 3025, then the value of 2 3 + 4 3 +.....+ 20 3 is :
Correct Answer

(C) 24200

Explanation

Solution: ∵ 1 3 + 2 3 + .....+ 10 3 = 3025 To find = 2 3 + 4 3 + 6 3 +.....+ 20 3 = ? ⇒ 2 3 (1 3 + 2 3 + .....+ 10 3 ) ⇒ 8 × 3025 ⇒ 24200