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What is the smallest positive integer that can be multiply..

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What is the smallest positive integer that can be multiply..

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What is the smallest positive integer that can be multiply by 1,008 to make it a perfect square?

A. 2
B. 3
C. 5
D. 7
E. 11

The OA is D.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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GMAT/MBA Expert

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Hello LUANDATO.

Let's take a look at your question.

One easy way to solve this PS question is trying number by number.

Option 1: 2*1,008 = 2016, is not a perfect square.

Option 2: 3*1,008 = 3024, is not a perfect square.

Option 3: 5*1,008 = 5040, is not a perfect square.

Option 4: 7*1,008 = 7056 = (84)^2, is a perfect square.

Hence, the correct option is the option D.

-----------------------------------------------------------------------------

Another way to solve it is: $$1008=2^4\cdot3^2\cdot7.$$ To have a perfect square we need an even number of 2's, 3's and 7`s.

So, we need to multiply 1008 to have 2 sevens. This is why the correct option is D.

I hope these explanations may help you.

Feel free to ask me again if you have any doubt.

Regards.

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