Ncert solutions

# Question 4

Q1. 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.

(c) A number is divisible by 18 if it is divisible by both 3 and 6.

(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.

SOLUTION:

i) false because there are plenty of numbers that are divisible by 3 but not divisible by 9. eg.30.

ii) true

iii) false, number 30 for example, is divisible by 3 and 6 but not divisible by 18.

iv) true

v) false, we know that two numbers having only 1 as a common factor are called co.prime numbers, so not necessary that one of them must be prime.

vi) false, example number 36 is divisible by 4 but not divisible by 8.

vii) true

viii) true

ix) false, example number 5 exactly divides the sum of two number 2 and 3 but not exactly divide these two numbers.

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