If the positive integer x is a multiple of 8 and 12, then x must be a

Question

If the positive integer x is a multiple of 8 and 12, then x must be a multiple of which of the following?

I. 24
II. 48
III. 96

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

gmatophobia · Answer

This a MUST be true question, hence we need to ensure that the answer choice holds true for all conditions.

Given

x is multiple of 8 
 Inference: x has  2^3  in its prime factorized form 
 
 x is a multiple of 12
 Inference: x has  2^2 * 3  in its prime factorized form

Using the above two statements, we can conclude that x has at least  2^3 * 3  in its prime factorized form.

Therefore x must be divisible by 8 * 3 = 24.

We cannot conclude anything apart from this.

Hence   Option A

SwethaReddyL · Answer

Bunuel , if x is a mul of 8 and 12, it should be a mul of it's lcm which is 24. 
Both 48 and 96 are mul of 24, why are they not included?

Bunuel · Answer

Because the direction matters.

48 and 96 are multiples of 24, but not every multiple of 24 is a multiple of 48 or 96.

x could be 24. It is a multiple of both 8 and 12, but it is not a multiple of 48 or 96.

So x must be a multiple of 24 only.

Answer: A.

If the positive integer x is a multiple of 8 and 12, then x must be a

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GMAT Problem Solving (PS) Questions

If the positive integer x is a multiple of 8 and 12, then x must be a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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