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Question on Perfect Square 9

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by richachampion » Mon Oct 17, 2016 3:20 am
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000
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by richachampion » Mon Oct 17, 2016 3:21 am
OA: B

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by Brent@GMATPrepNow » Mon Oct 17, 2016 6:22 am
richachampion wrote:Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100,000
Start with perfect squares that are CLOSE to each answer choice.

A) 649
We know that 25² = 625.
So, perhaps 26² = 649?
NO.
Here's a quick reason why.
25² = (25)(25) = 625
(25)(26) = (25)(25 + 1) = 625 + 25 = 650
So, 26² will be GREATER THAN 650. So 26² CANNOT equal 649

Alternatively, the units digit of 26 is 6, so 26² will have units digit 6 (since 6x6 = 36), but answer choice A has units digit 9
ELIMINATE A

B) 961
We know that 30² = 900.
So, perhaps 31² = 961?
Well, the units digit of 31 is 1, so 31² will have units digit 1. So, we have a definite contender.
Let's check this one.
31² = 961 BINGO!

Answer: B

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Brent
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by Matt@VeritasPrep » Fri Oct 28, 2016 12:55 am
I'd look for nearby perfect squares: it's no coincidence that the answers are all close to easy squares (900, 1600, 2500, etc.) Let's also cheat here with a nice identity:

(x + 1)*(x + 1) = x*x + 2x + 1

So if we have x², we can get to the next square by adding 2x + 1.

900 is a great candidate. 30² = 900, so the next square is 900 + 2*30 + 1, or ... 961! :D
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