Which of the following number is divisible by both 3 and 9?

192

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720

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285

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2398

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Solution

The correct option is B 720
A number is divisible by 3 and 9 if the sum of the digits is divisible by 3 and 9 respectively.

192
Sum of the digits = 1 + 9 + 2 = 12
12 is divisible by 3 but not by 9. Hence, 192 is divisible by 3 but not divisible by 9.

720
Sum of the digits = 7 + 2 + 0 = 9
9 is divisible by both 3 and 9. Hence, 720 is divisible by both 3 and 9.

285
Sum of the digits = 2 + 8 + 5 = 15
15 is divisible by 3 but not by 9. Hence, 285 is divisible by 3 but not divisible by 9.

2398
Sum of the digits = 2 + 3 + 9 + 8 = 22
22 is not divisible by both 3 and 9. Hence, 2398 is not divisible by both 3 and 9.

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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.

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(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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