Is the positive integer x a multiple of 16?

Question

(1) x is a multiple of 8.
(2) x^2 is a multiple of 32.

GMATBusters · Answer

S1: x can be 8 or 16: not sufficient. 
S2: x^2 is multiple of 32: 2^5. that means x can be 8 or 16. Not sufficient. 
Even combination of statement 1&2 doesn't give any new info. 
Hence insufficient. 
Answer is E.

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GMATBusters · Answer

S1: x can be 8 or 16: not sufficient. 
S2: x^2 is multiple of 32: 2^5. that means x can be 8 or 16. Not sufficient. 
Even combination of statement 1&2 doesn't give any new info. 
Hence insufficient. 
Answer is E.

Posted from my mobile device

amanvermagmat · Answer

For a number to be divisible by 16, that number must have at least four 2's in its prime factorisation (because 16 = 2^4).

(1) x is a multiple of 8, or of 2^3. This guarantees that x has at least three 2's, but we cant say about four 2's. Insufficient.

(2) x^2 is a multiple of 32, or of 2^5. Now since x is a positive integer, x^2 is a perfect square, which means all powers of prime numbers in prime factorisation of x^2 will be even. So x^2 cannot just have five 2's, if its a multiple of 32 (2^5), it will have at least six 2's.(x^2 will be at-least 2^6). This in turn tells us that x will be at least 2^3, or we can say that x is a multiple of 8. Same as first statement. Insufficient.

Since both statements tell us the same thing, even after combining them we cant say whether x has more than three 2's or not. So Insufficient.

Hence  E answer

spetznaz · Answer

+1 for option E.

St 1 - NS
St 2 - NS ; x is of the form 8k. (bçoz - if x^2 =32k ; x will have one factor of 4 and one factor of 2 to be a perfect square).

Both together - NS
The answer is option E

Is the positive integer x a multiple of 16?

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