If a is an integer and a^2/12^3 is odd, which of the following must be

Question

If a is an integer and  \frac{a^2}{12^3}  is odd, which of the following must be an odd integer?

A. a/4
B. a/12
C. a/27
D. a/36
E. a/72

beeunoia · Accepted Answer

Here we will consider solely int numbers

\frac{a^2}{12^3}  = odd

A. Let's check if the answer is 1

\frac{x^2}{12^3}  = 1

x^2 = 1*12*12*12

x = \sqrt{12*144}

x = 12 * \sqrt{12}

x = fraction - insufficient

B. Let's check if the answer is 3

\frac{x^2}{12^3}  = 3

x^2 = 3*12*12*12

x = \sqrt{36*144}

x = 6*12

x = 72

C. Let's check answers

A. a/4 = 72/4 = even
B. a/12 = even
C. a/27 = not int
D. a/36 = even
 E. a/72 = odd

Option E is correct!

Bunuel · Answer

\frac{a^2}{12^3}=odd ;

a^2=12^3*odd=12^2*(2^2*3)*odd ;

a=24\sqrt{3*odd} .

Notice that the least positive value of a is  a=24\sqrt{3*3}=72  (if that odd integer is 3) and if a is 72, then only option E gives and odd integer, hence it must be correct.

Answer: E.

hykhan · Answer

Here's how I solved it.

1) first thing to know is that 12^3 will give you an even number since even numbers to any exponent produce even numbers. Therefore, in order to get an odd value, the numerator must be an even number.

- Eliminate C as a result (even divided by odd will NEVER be an odd integer, since odd x odd = odd).

2) Because the numerator is squared, the value must be greater than 12, since it needs to be divisible by 12^3 power. This is the second hint. There are many multiples of 12 that suffice a and when divided by 12, will yield an integer. Some of them are odd, some are even. We are looking for a value that MUST be ODD. Eliminate B

3) Because 4 is a factor and thus smaller than 12, the same logic as above applies to eliminate A.

4) We're left with 36 and 72. (36)(36)/(12)(12)(12) does not give you an integer, since the two 36 values divided by two 12s would leave two 3s, and 9/12 is not an integer and does not fit with the question stem. therefore, D is eliminated. The answer you're left with is E.

5) As a proof, if you try 72, you will see that (72)(72)/(12)(12)(12) leaves you with two 6s, and 36/12 = 3 which fits the question stem. Now, looking at the value, the only way 72 can be divided and ALWAYS give you an odd value is if 72 is divided by 72. Hence E

I know its a lot of writing, but this kind of all happens in your head with a bit of reasoning.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a is an integer and a^2/12^3 is odd, which of the following must be

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a is an integer and a^2/12^3 is odd, which of the following must be

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards