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The LCM of three numbers is four times their GCF. Which of

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The LCM of three numbers is four times their GCF. Which of

by Gmat_mission » Sun Jun 30, 2019 9:11 am

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The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be the same.
III. At least one number is the same as GCF.

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

[spoiler]OA=B[/spoiler]

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by Ian Stewart » Mon Jul 01, 2019 6:43 am
The numbers could be 2, 4, and 8, so I and II need not be true. That leaves only answer B.
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by Scott@TargetTestPrep » Tue Jul 02, 2019 5:41 pm
Gmat_mission wrote:The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be the same.
III. At least one number is the same as GCF.

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

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

If the three numbers are 4, 8 and 16, the LCM is 16 and the GCF is 4. We see that 16 is four times 4, but neither any of the numbers is odd nor two of them are the same. Thus, we see that I and II are not true. We see that III can be true since 4 is one of the three numbers. Without analyzing III further, by looking at the given answer choices, we can reject A, C, D and E; therefore, we are left with B as the correct answer.

Answer: B

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by GMATGuruNY » Wed Jul 03, 2019 2:19 am
Gmat_mission wrote:The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be the same.
III. At least one number is the same as GCF.

A. I only
B. III only
C. I and III only
D. I and II only
E. II and III only
Try to prove that I, II and III DON'T have to be true.

To disprove I -- which states that at least one number must be odd -- let the GCF = 2.
Since the LCM = 4(GCF), the LCM = 8.
In this case:
The greatest factor common of all three numbers must be 2.
The least value divisible by all 3 numbers must be 8.
Thus, the three numbers could be 2, 4 and 8.

Since none of the numbers here are odd, eliminate any answer choice that includes I (A, C, and D).
Since all 3 numbers are different, eliminate any remaining answer choice that includes II (E).

The correct answer is B.
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