Which one of the following numbers is exactly divisible by 11?

(a) 235641
(b) 245642
(c) 315624
(d) 415624

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Solution

(d) 4,15,624
Sum of digits at odd places = 4 + 5 + 2 = 11
Sum of digits at even places = 1 + 6 + 4 = 11
Difference of these two sums = 11 − 11 = 0
Therefore, 4,15,624 is divisible by 11.

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Which of the following statements are true?

(a) If a number is divisible by 3, it must be divisible by 9.

(b) If a number is divisible by 9, it must be divisible by 3.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) If two numbers are co-primes, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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