If positive integer x is a multiple of 14 and 12, which of the followi

X is a multiple of 12 and 14, Then X must be in the form of 2^2*3*7*k, where k is an positive integer.

1. If k is odd, X can't be multiple of 8
2. X=2^2*3*7*k= 28*3k, hence always a multiple of 28
3. If k is multiple of 3, then GCD(x,9)= 9

Only 2nd statement must be true

LCM Of 14 and 12 is 84.

So x would be multiple of 84 such as 84*1, 84*2, ....,84*8 etc


1) x may or may not be divisible by 8
2) x is surely divisible by 28 because 84 is divisible by 28.
3) GCF of x and 9 can be 3 or or 9 based on what value of x in above mentioned possibilities.

So 2 only must be true.

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We recall that if a number is a multiple of two numbers, it’s also a multiple of the LCM of the two numbers. The LCM of 14 and 12 is 7 * 4 * 3 = 84. So x is a multiple of 84.

We also recall that if a is a multiple of b, then it’s also a multiple of any factors of b.

Thus, we see that x MUST BE divisible by 28 (since 28 is a factor of 84) but not necessarily by 8 (since 8 is not a factor 84). Thus, we see that statement I is not necessarily true, and statement II must be true.

The GCF of x and 9 does not have to be 3. For example, if x = 84 * 3 = 252, then the GCF of x and 9 is 9. Thus, statement III is not necessarily true.

Answer: B
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The question would be more logical if the question were

If positive integer x is divisible by both 14 and 12, which of the following statements must be true?

I started thinking 12*14

whose prime factorization is 7*3*\(2^3\)

Do we get this kinda question in GMAT??

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