Problem Solving

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

Did you get the question right?

I did not get the question right. BTW the answer is C but I don't get it.

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.

I feel the same way - there's something funky about that question.

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

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!

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

thanks, everyone

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.

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.

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.