If k is a positive integer whose only prime factors are 2 and 5, is k

Question

If k is a positive integer whose only prime factors are 2 and 5, is k divisible by 20?

(1) k is a multiple of 16
(2) k has 6 factors

RohitKakkar · Answer

Answer A

K = 2^a X 5^b for K to divide by 20 k should have a=>2 and b=>1

A K is a multiple of 16 it means K=2^4 X I condition is satisfying

B K has 6 factors 
2^2X5 then answer is yes

But 2X5^2 then answer is no

Hence answer is A

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Bunuel · Answer

If k is a positive integer whose only prime factors are 2 and 5, is k divisible by 20?

k is a positive integer whose  only  prime factors are 2 and 5:  k=2^x*5^y , where  x\geq{1}  and  y\geq{1}  ( notice that the number of factors of k would be (x + 1)(y + 1) ). Also notice that k will be divisible by  20 = 2^2*5  if  x\geq{2}  and  y\geq{1}  (this condition is already satisficed from the stem). So, the question basically asks whether  x\geq{2} .

(1) k is a multiple of 16. 16 = 2^4, hence this statement implies that  x \geq{4} . Sufficient.

(2) k has 6 factors --> this means that (x + 1)(y + 1) = 6. If x = 2 and y = 1, then the answer will be YES but if x = 1 and y = 2, then the answer will be NO. Not sufficient.

Answer: A.

Hope it's clear.

If k is a positive integer whose only prime factors are 2 and 5, is k

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