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Which of the following is not a perfect square?

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by Gmat_mission » Sun Jun 24, 2018 11:45 pm
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Which of the following is not a perfect square?

1. 100856
2. 325137
3. 945729
4. All of these
5. None of these

[spoiler]OA=D[/spoiler]

Could someone give me the best approach to solve this PS question? Please.
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by Jeff@TargetTestPrep » Tue Jun 26, 2018 5:21 pm
Gmat_mission wrote:Which of the following is not a perfect square?

1. 100856
2. 325137
3. 945729
4. All of these
5. None of these
We know that a perfect square must end with 0, 1, 4, 5, 6, or 9, so we can see choice 2 is not a perfect square.

Now let’s check choice 1. Since 310^2 = 96,100 and 320^2 = 102,400, then, if 100,856 is a perfect square, it must be the square of either 314 or 316 since either one of these integers will produce a units digit of 6 when squared. However, since 314^2 = 98,596 and 316^2 = 99,856, we see that choice 1 is a not a perfect square, either.

Since both choices 1 and 2 are not perfect squares, we will conclude that the correct answer must be choice 4 (even though we have not verified that choice 3 is not a perfect square).

Answer: 4

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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