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Problem Solving Question

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Problem Solving Question

by amidoshi » Tue Aug 16, 2011 9:20 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
I only
II only
I and II only
II and III only
I, II, and III

I understand the II cannot be an answer, but I don't understand what III cannot be included. 48 is divisible by 3, 8, and 12.

Please help!
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by sumgb » Tue Aug 16, 2011 10:19 am
If y = 24. Is 24 divisible by 48? there's your answer...

hope this helps.
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by gmatboost » Wed Aug 17, 2011 2:14 pm
Sumgb gave a good answer to why 48 is not included

The thorough approach to the question:
3 = 3
8 = 2^3
12 = 2^2 * 3

To capture all of these the pieces we MUST have are 3*(2^3) = 24
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by amidoshi » Wed Aug 17, 2011 3:38 pm
So, because 48 has 4 instances of 2, it cannot be confirmed that y will be divisible by 48? Sumgb's answer confused me because 48 is divisible by 24 so I would assume that y would also be divisible by 48.

Or, is it that because 48 is already divisible by 24 we don't need to include it in the list?
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by winniethepooh » Wed Aug 17, 2011 7:53 pm
The question is asking you to find an answer which of the option must Y be divisible by?

The answer is simply the LCM of the three numbers(this answer alone satisfies the MUST criteria)
That is 24.
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by gmatboost » Wed Aug 17, 2011 8:38 pm
Amidoshi,

All we know is that Y must be divisible by 3, 8, and 12

That means it must be divisible by 3, 2^3, and 2^2 * 3
This in turn means it MUST be divisible by 3*(2^3)

Could it be divisible by 2^4? Maybe, but we don't know for sure. There is no reason it MUST be divisible by that.

The clearest example of this is 24, which meets all the conditions (divisible by 3, 8, and 12). So 24 could be Y. And 24 is NOT divisible by 48. This gives a numerical demonstration that while Y MIGHT be divisible by 24, there is no reason it MUST be.
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by krishna8143 » Wed Aug 17, 2011 10:24 pm
simple and common logic for all these type of problems is when the num. is divisable by some different numbers, it must divisible by L.C.M of those numbers

so as in this case lcm of 3,8,12 is 24

so the ans is 24
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