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 Post subject: Data Sufficiency (Vol. VIII), Question #77.Posted: Sat Oct 30, 2010 3:23 pm

Joined: Thu Jul 01, 2010 12:05 am
Posts: 35
This question asks the following: "If y is an integer, is y² divisible by 4?"

(1) y is even
(2) y³ is divisible by 4.

The correct answer is D, because either one of these statements are sufficient to answer the question. I don't understand how the second statement is sufficient to answer the question. For instance, the solution explains that "if y³ can be divided by 4, then y must have a multiple of 2." Can you explain this part in more detail, please?

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 Post subject: Re: Data Sufficiency (Vol. VIII), Question #77.Posted: Wed Nov 03, 2010 11:51 am

Joined: Thu Jul 03, 2008 2:13 pm
Posts: 117
Good question! If y^3 is divisible by 4, then that means that y^3 is divisible by 2 * 2.

Now, because y^3 is y*y*y, it has to be a "symmetrical" number - each y has to be exactly the same, and so for one y to be divisible by 2, then each other y must be divisible by 2. And if we know that y is an integer, as the statement has told us, then for y*y*y to be divisible by 2*2, then y must be divisible by 2 as we've removed the possibility for a decimal version of y to cube out to 4 or 12.

The fact that y is an integer is crucial here - if not, a noninteger could conceivably cube to 4 (there is, indeed, a cube root of 4), but since y is an integer then we know that each individual y must divide by a 2 as shown above, so y is divisible by 2.

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