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Which of the following numbers is a perfect square?

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by gmattesttaker2 » Fri May 02, 2014 5:48 pm
Hello,

Can you please help with this:

Which of the following numbers is a perfect square?

A) 1266

B) 1444

C) 2022

D) 4034

E) 8122


OA: B

This is from Veritas Prep. I was not clear with the official explanation though. Thanks a lot.

Best Regards,
Sri
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by Quasar Chunawala » Fri May 02, 2014 11:15 pm
Strictly based on number theory learnt in GMAT alone, I don't know a quick way to check perfect squares. However, based two special number properties, here's a fast way to do it -

1. Perfect squares always end in 1,4,5,6,9. Eliminate choices (C) and (E).
2. Digital roots of a perfect square are from {1,4,7,9}. Digital root is the sum of all digits of a number.
1+2+6+6 => 15 => 1+5 => 6(Not a perfect square)
1+4+4+4 => 13 => 1+3 => 4(Could be a perfect square)
4+0+3+4 => 11 => 1+1 => 2(Not a perfect square).

Option (B) 1,444 is a perfect square. Its square root is between 30 and 40. It could be either 32 or 38(last digit =4). Since, 1444 is closer to 1600 than it is to 900, 38^2 = 1444.
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