$31 x 5 divisible by 3 ?$

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Solution

$∵ 31 x 5 is divisible by 3 \Rightarrow 3 + 1 + x + 5 is a multiple of 3 \Rightarrow 9 + x = 0, 3, 6, 9, . . . . \Rightarrow x = - 9, - 6, - 3, 0, 3, 6, 9, . . . . Since, x is a digit ∴ x = 0, 3, 6 o r 9$

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Question 31
A number is divisible by 5 and 6. It may not be divisible by

(A) 10
(B) 15
(C) 30
(D) 60

31 m 4

3

m

3 \frac{1}{5}

\frac{3}{5}

31

5

Show that:

$(i) 13^{3} - 5^{3}$ is divisible by 8.

$(i i) 35^{3} + 27^{3}$ is divisible by 62.

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