Question on Perfect Square 9

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

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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Source: Beat The GMAT — Problem Solving | Mon Oct 17, 2016 3:20 am

richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Mon Oct 17, 2016 3:21 am

OA: B

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Target Score: 760+
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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 25Â² = 625.
So, perhaps 26Â² = 649?
NO.
Here's a quick reason why.
25Â² = (25)(25) = 625
(25)(26) = (25)(25 + 1) = 625 + 25 = 650
So, 26Â² will be GREATER THAN 650. So 26Â² CANNOT equal 649

Alternatively, the units digit of 26 is 6, so 26Â² will have units digit 6 (since 6x6 = 36), but answer choice A has units digit 9
ELIMINATE A

B) 961
We know that 30Â² = 900.
So, perhaps 31Â² = 961?
Well, the units digit of 31 is 1, so 31Â² will have units digit 1. So, we have a definite contender.
Let's check this one.
31Â² = 961 BINGO!

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

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 xÂ², we can get to the next square by adding 2x + 1.

900 is a great candidate. 30Â² = 900, so the next square is 900 + 2*30 + 1, or ... 961!

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