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If A and B are positive integers and 12AB is a perfect

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Senior Manager
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If A and B are positive integers and 12AB is a perfect [#permalink]

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11 Sep 2004, 14:21
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If A and B are positive integers and 12AB is a perfect square, then which of the following cannot be the possible values for A and B?

(1) A = 6, B = 6
(2) A = 8, B= 18
(3) A = 9, B = 25
(4) A = 9, B = 36
(5) A = 12, B = 48

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11 Sep 2004, 15:53
I have calculated them all, and neither has an perfect square as solution.

Are you sure it is 12 * A * B is an perfect square?

But....it could be that I am doing something wrong.

Correct me please if I am wrong.

Regards,

Alex

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11 Sep 2004, 16:08
Alex, I got the same. I broke them down to their prime numbers
12 = 2*2*3
To have a perfect square, we need an odd number of 3's and an even number of 2's for A*B combined which none of the answers have. Actually, all of the answers cannot give a Perf. sq. for 12AB
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Paul

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11 Sep 2004, 16:20
Exactly, I used the same method.

Gmatblast,
Is this question also from Peterson?
Posting mistakes is not a problem for me, cause I think in that way it is also possible to learn strategies and techniques. But if this problem is also coming from Peterson....

Regards,

Alex

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11 Sep 2004, 17:03
I didn't calculate 12AB.

But for 12AB to be a perfect square, A abd B should have 3, 4, and A (where A may be 1 or any other perfect square). The 3 and 4 are needed to square the 3 and 4 already present in 12).

In that way C is the odd man out.

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11 Sep 2004, 17:29
hardworker, C cannot be a perfect sq. because 9 is 3*3 and if you multiply that by the 3 from 3*4*AB, you now have 3x3's which cannot give a perfect sq.
As a matter of fact, 12*9*25=2700
52^2 = 2704
51^2 = 2601
Hence, C is just like any other answer and is NOT a perfect sq.
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Paul

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11 Sep 2004, 18:09
I wanted to veryfy that this question is not correct. And I think everybody's response here has done just that I Peterson does a lot of guffy things.

By the way the answer is C. The explanation is: in order for 12AB to be a perfect sqaure AB should be multiple of 12. In C, AB is not multiple of 12 so the answer. But this reasoning is clearly wrong.

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11 Sep 2004, 20:51
1.
Paul wrote:
hardworker, C cannot be a perfect sq.

Yes, I think we are saying the same. The question also askes for an EXCEPT choice - "which of the following cannot be the possible values for A and B".

2. And yes, I agree that the Q is wrongly worked.
The theory that was supposed to be tested is, "12 is already a part of 12AB. To make 12AB perfect square, AB should surely include another 12 (to make it square), among other factors which should be square themselves."
All other choices have a 4 and 3 n AB, making up for the 12 to be square. Only C lacks a 4, and is hence odd man out.

As I have seen before, if the question is wrongly worded/worked out, we can discuss and reject convincingly in forums. But on the real test, if such a problem pops up, we have to choose an answer to move on. In that case, it can be C, the odd man out. After all, all we care for is marks

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11 Sep 2004, 20:51
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