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If the positive integer y is divisible by 3, 8, and 12,

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by M7MBA » Sat Feb 03, 2018 6:52 am
If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?

I. 24
II. 36
III. 48

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

The OA is the option A.

I don't understand. Why y is not divisible by 36 if y is divisible by 3 and 12. I don't understand. Experts, can you help me here?
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by EconomistGMATTutor » Sat Feb 03, 2018 7:55 am
M7MBA wrote:If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?

I. 24
II. 36
III. 48

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

The OA is the option A.

I don't understand. Why y is not divisible by 36 if y is divisible by 3 and 12. I don't understand. Experts, can you help me here?
Hello M7MBA.

Now, since y is divisible by 3, 8 and 12, we get that y has, on its prime factorization, three 2's and one 3. This is becuase

3 = 3*1
8 = 2*2*2
12 = 2*2*3

LCM(3,8,12) = 3*2*2*2 = 24.

Hence, y is divisible by 24.

Now, y is not divisible by 36 because 36 = 2*2*3*3, and y only have one 3 on its prime factorization.

At the same way, 48 = 2*2*2*2*3, but y only has three 2's on its prime factorization.

Therefore, the correct answer is the option A.

I hope this answer may help you to clarify your doubt.

I'm available if you'd like a follow-up.

Regards.
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by [email protected] » Sat Feb 03, 2018 10:52 am
Hi M7MBA,

We're told that the positive integer Y is divisible by 3, 8, and 12. We're asked which of the following MUST Y be divisible by. In these types of questions, it's often best to find the smallest value that 'fits' everything that we're told - then we can compare THAT value to the options given.

Even if you're not familiar with prime factorization, you can still find the least possible value of Y with a bit of 'brute force' math:

Multiples of 12: 12, 24, 36....
Multiples of 8: 8, 16, 24, 32....

Notice how 24 is both a multiple of 12 and 8? Is it also a multiple of 3? YES (3x8 = 24), so the smallest possible value of Y is 24. Using that value, we can compare against the three Roman Numerals...

I. Is 24 a multiple of 24? YES
II. Is 24 a multiple of 36? NO
III. Is 24 a multiple of 48? NO

Final Answer: A

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by Jeff@TargetTestPrep » Fri Feb 09, 2018 10:18 am
M7MBA wrote:If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?

I. 24
II. 36
III. 48

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
The LCM of 3, 8, and 12 is 24. So y must be 24 or a multiple of of 24. Let's test each answer choice.

We see that Roman numeral I is correct; if y = 24, then y/24 = 24/24 = 1.

Roman numeral II is not a multiple of 24, so it is not correct.

You might think that Roman numeral III, the value 48, should be correct, but it isn't. If y were equal to 24, then y is NOT divisible by 48, because y/48 = 24/48 does not yield an integer as the answer.

The only answer that MUST be correct is y = 24.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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