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perfect square problem

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perfect square problem

by robk100 » Thu Jan 17, 2008 5:27 pm
If A and B are positive integers and 12AB is a perfect square, then which of the following CANNOT be possible values for A and B?

A) A=6, B=6
B) A=8, B=8
C) A=9, B=25
D) A=9, B=36
E) A=12, B=48

I'm under the impression that perfect square means you can take the square root of the number and get a whole number. But it doesn't seem like 12AB produces any perfect squares. Am I misinterpreting the problem? help please!

Thanks
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by StarDust845 » Fri Jan 18, 2008 9:51 am
Did you get the question right?
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by robk100 » Fri Jan 18, 2008 2:56 pm
I did not get the question right. BTW the answer is C but I don't get it.
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by StarDust845 » Fri Jan 18, 2008 3:16 pm
robk100 wrote:I did not get the question right. BTW the answer is C but I don't get it.
No, I am not asking whether you answered the question right. I am asking whether the question you have posted is correct? Can you double check? Because for none of those values 12AB is a perfect square.
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by solaris » Fri Jan 18, 2008 3:25 pm
I feel the same way - there's something funky about that question.
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by II » Fri Jan 18, 2008 4:02 pm
I agree guys ...

Robk100 ... where did you get this question from ? can you please double check it ?

Another question:
What is the quickest way to find out if a number is a perfect square or not ?
For example, take 12384. How would you find out if this number was a perfect square quickly ?
Any quick shortcuts to finding perfect squares out there ?

Thanks.
II
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Re: perfect square problem

by Stuart@KaplanGMAT » Fri Jan 18, 2008 6:58 pm
robk100 wrote:If A and B are positive integers and 12AB is a perfect square, then which of the following CANNOT be possible values for A and B?

A) A=6, B=6
B) A=8, B=8
C) A=9, B=25
D) A=9, B=36
E) A=12, B=48

I'm under the impression that perfect square means you can take the square root of the number and get a whole number. But it doesn't seem like 12AB produces any perfect squares. Am I misinterpreting the problem? help please!

Thanks
There's definitely something wrong with the question.

12AB means 12*A*B

For any number to be a perfect square, it has to be composed of pairs of primes.

For example, 2*2, 3*3, 2*2*3*3, 7*7*11*11 will all be perfect squares;

while 2*3*3, 3*5, 5*5*7 will not be perfect squares.

So, we need to break 12AB down into primes.

12 = 2*2*3. Therefore, in order for 12AB to be a perfect square, we need one more 3 and the rest of AB has to be made up of pairs of primes.

Let's look at the choices:

(A) a=6, b=6 so 12AB = 2*2*3*2*3*2*3... odd # of 3s, not a PS

(B) a=8, b=8 so 12AB = 2*2*3*2*2*2*2*2*2... odd # of 3s, not a PS

(C) a=9, b=25 so 12AB = 2*2*3*3*3*5*5... odd # of 3s, not a PS

(D) a=9, b=36 so 12AB = 2*2*3*3*3*2*2*3*3... odd # of 3s, not a PS

(E) a=12, b=48 so 12AB = 2*2*3*2*2*3*2*2*2*2*3... odd # of 3s, not a PS

soo.. none of the answers can be PSs, they're all correct!
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re:

by robk100 » Sat Jan 19, 2008 6:56 pm
I printed the question exactly how it came in the book. It's from the Insider's Guide to the GMAT CAT. I believe it was from the problem solving section 2, problem #4. And it said something about 25X9 is not divisible by 12 therefore the answer must be C. I guess the book made an error. Thank you for all your replies
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by yalephd2007 » Sun Apr 13, 2008 9:05 am
thanks, everyone
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by shaz » Fri May 09, 2008 1:46 am
The problem is as simple as no perfect square can end with 2,3,7 and 8.
So B AND E can be the answers.for others I dont know.
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Re: perfect square problem

by dorian_alb » Thu Oct 01, 2009 11:14 am
robk100 wrote:If A and B are positive integers and 12AB is a perfect square, then which of the following CANNOT be possible values for A and B?

A) A=6, B=6
B) A=8, B=8
C) A=9, B=25
D) A=9, B=36
E) A=12, B=48

I'm under the impression that perfect square means you can take the square root of the number and get a whole number. But it doesn't seem like 12AB produces any perfect squares. Am I misinterpreting the problem? help please!

Thanks

I think the right answer is E, i.e. when A=12 and B=48, 12*A*B CANNOT be a perfect square.

Here is the reasoning:

When A=12, 12*A*B can be a PS only if B=1 (or other numbers like 144) because 12*12*1= 144. It is given that A=12. So I think B must be equal to 1. Perhaps it could be equal to other numbers like 144 itself, but for sure it is not 48.

So the other case is 12*A*B=12*12*144. B is either 1 or 144, as I see it, but not 48.

I'm not 100% sure though, guys. Any other possible solutions appreciated. :)

Take care,
d.
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by pradeep1982 » Fri Jul 01, 2011 9:42 am
hi,

i m new to this forum first of all thank you for this beautiful forum

The answer to this problem will be C option as follows :

if the last two digits of perfect square are 25 then the no can only end with 5.

now as per option C - no is 12925

so 129 & 25 --->

25 --> 5

but 129 -- 43 x 3 here 43 is prime no so 129 cannot be converted into perfect square.

so with 9 & 25 of option C --- perfect square no possible.
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