If 6 is a factor of a and 21 is a factor of b, is ab a multiple of 70?

Question

(1) a is a multiple of 4.
(2) b is a multiple of 15.

IanStewart · Answer

ab will be a multiple of 70 if ab is divisible by 2, 5 and 7. Since a is divisible by 6, we know ab is divisible by 2, and since b is divisible by 21, we know ab is divisible by 7. The only thing we don't know is if ab is divisible by 5. Statement 1 is no help there, but Statement 2 tells us b is divisible by 5, so it is sufficient, and the answer is B.

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LevanKhukhunashvili · Answer

Known prime factors of  a  2 and 3
Known prime factors of  b  3 and 7

Known prime factors of  ab  2, 3, 7
ab will be multiple of 70 if we prove that ab has 2, 5, 7 as primes
According to the stem ab has 2 and 7 as factors, so we need to know whether ab has 5 as it's prime factor

1 stm -->  insuff 
2 stm --> b has 5 as a factor.  suff

IMO
Ans:  B

If 6 is a factor of a and 21 is a factor of b, is ab a multiple of 70?

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