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by vinay1983 » Thu Sep 26, 2013 7:00 am
The Least Common Multiple of three numbers is four times their Greatest Common Factor. 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 same.
III. At least one number is the same as Greatest Common Factor.

1. I only
2. III only
3. I and III only
4. I and II only
5. II and III only
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by theCodeToGMAT » Thu Sep 26, 2013 9:23 am
x = a
y = a x 4
z = a x 4
GCD = a
LCM = a x 4

Statement 1: "a" could be even or odd
For instance:
x = 3
y = 3x4
z = 3x4
GCD = 3
LCM = 12

AND

x = 4
y = 4x4
z = 4x4
GCD = 4
LCM = 16
INVALID

Statement 2: Two numbers are same..
x = a
y = a x 2
z = a x 4
INVALID

Statement 3: At least one number is the same as Greatest Common Factor.
x = a
y = a x4
z = a x2
If one number were not equal to GCD then GCD would be different.

Hence {2}
what is the OA?
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by [email protected] » Thu Sep 26, 2013 11:48 am
Hi vinay1983

While this question is a bit more complex than normal, you can beat it by TESTing values and attempting to DISPROVE the Roman Numerals:

We're told that there are 3 numbers with an LCM = 4(GCF)

That "4" in the equation gives us a clue as to what the 3 numbers COULD be....(hint: think about including the number 4)

If we used 1, 2 and 4, then the LCM = 4 and the GCF = 1. This fits perfectly with what we were told. With these values, we've disproved II. Eliminate D and E.

If we used 2, 4, 8, then the LCM = 8 and the GCF = 2. This also fits with what we were told. With these values, we've disproved I. Eliminate A and C.

Final Answer: B

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by GMATGuruNY » Fri Sep 27, 2013 2:03 am
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 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


Kindly elaborate the approach .. regards!

OA B
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.
Last edited by GMATGuruNY on Tue Dec 08, 2015 11:00 am, edited 1 time in total.
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by Brent@GMATPrepNow » Fri Sep 27, 2013 6:18 am
I'd like to point out an important feature of this question.
Notice that, once we've shown that statements I and II are not necessarily true, we are able to eliminate answer choices A, C, D and E. So, the answer must be B.

So, we can reach the correct answer WITHOUT EVEN LOOKING AT statement III.
In fact, if we bother looking at statement III, we're wasting time.

So, for these kinds of multi-statement questions, be sure to eliminate answer choices each time to reach a conclusion about a statement.

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by faraz_jeddah » Sat Sep 28, 2013 8:09 am
Good question!
A good question also deserves a Thanks.

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by vinay1983 » Sat Sep 28, 2013 8:17 am
faraz_jeddah wrote:Good question!
True to your words aren't you faraz!

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You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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