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neeti1813
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 official solution is overly complicated for no reason.

y needs to be divisible by 3, 8 and 12. This means that it must be the LCM of 3, 8 and 12 or a multiple of the LCM. The LCM is the smallest number which is divisible by all 3 numbers.

LCM of 3, 8 and 12 will be 3*8 = 24

Now y must be either 24 or a multiple of 24. In any case it will always be divisible by 24.
Will it be divisible by 36 necessarily? No. Say if y is 24, it will not be divisible by 36.
Will it be divisible by 48 necessarily? No. Say if y is 24, it will not be divisible by 48.

Answer (A)
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neeti1813
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
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Hello from the GMAT Club BumpBot!

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