Which of the following statements are true?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must by divisible by 3.
(iii) If a number is divisible by 4, it must by divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.
(i) Right answer is False
Explanation:-
Because any number which follows the formula 9n + 3 or 9n + 6 violates the statement.
For example: 6, 12…
(ii) Right answer is True
Explanation:-
Because 9 is multiple of 3, any number divisible by 9 is also divisible by 3.
(iii) Right answer is False
Explanation:-
Because any number which follows the formula 8n + 4 violates the statement.
For example: 4, 12, 20….
(iv) Right answer is True
Explanation:-
Because 8 is multiple of 4, any number divisible by 8 is also divisible by 4.
(v) Right answer is False
Explanation:-
Because for example 24, this is divisible by both 3 and 6 but not divisible by 18.
(vi) IRight answer is True
Explanation:-
Because 90 is the GCD of 9 and 10, any number divisible by both 9 and 10 is also divisible by 90.
(vii) Right answer is False
Explanation:-
Because let us consider an example 6 divide 30, but 6 divides none of 13 and 17 as both are prime numbers.
(viii) Right answer is True
Explanation:-
Because if x, y and z are three numbers, each of x, y and z is divided by a number (say q), then (x + y + z) is also divisible by q.
(ix) Right answer is False
Explanation:-
Because 16 and 21 are co-prime but none of them is prime.
(x) Right answer is True
Explanation:-
Because 3+5=8 which is divisible by 4.
Answered by Aaryan | 1 year agoWhich of the following numbers are divisible by 11:
(i) 10835
(ii) 380237
(iii) 504670
(iv) 28248
In each of the following replace * by a digit so that the number formed is divisible by 11:
(i) 64 × 2456
(ii) 86 × 6194
In each of the following replace * by a digit so that the number formed is divisible by 6:
(i) 97 × 542
(ii) 709 × 94
In each of the following replace × by a digit so that the number formed is divisible by 9
(i) 49 × 2207
(ii) 5938 × 623
If 42z3 is a multiple of 9, where z is a digit, what is the value of z?