To find the perfect square

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

To find the perfect square

by gmattesttaker2 » Mon May 26, 2014 11:05 pm

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Hello,

For the following:

Which of the following is a perfect square?

A) 649
B) 961
C) 1664
D) 2509
E) 100000

OA: B

I was able to eliminate E since I could see that it was not a perfect square. I then started checking from A onwards. Here, B turned out to be a perfect square. I was just wondering if there is a better way to solve this problem? Thanks for your help.

Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Mon May 26, 2014 11:05 pm

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by [email protected] » Tue May 27, 2014 12:54 am

Hi Sri,

This is more of a "concept" question that a "calculation" question, although you do have to do some calculations to find the correct answer.

The way that you "saw" how E wasn't a perfect square is likely the same way that you knock out other answers. Here's how...

Consider answer D: 2509....

50 x 50 = 2500

51 x 51 would, at the very least, add ANOTHER 51 to the total, which would put that total past 2551. So there's no way to that 2509 would be a perfect square. This logic can be used to eliminate the other wrong answers as well (with varying degrees of "necessary" math).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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

by Brent@GMATPrepNow » Tue May 27, 2014 11:59 am

gmattesttaker2 wrote:Which of the following is a perfect square?

A) 649
B) 961
C) 1664
D) 2509
E) 100000

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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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

by gmattesttaker2 » Sat Jun 28, 2014 11:47 am

[email protected] wrote:Hi Sri,

This is more of a "concept" question that a "calculation" question, although you do have to do some calculations to find the correct answer.

The way that you "saw" how E wasn't a perfect square is likely the same way that you knock out other answers. Here's how...

Consider answer D: 2509....

50 x 50 = 2500

51 x 51 would, at the very least, add ANOTHER 51 to the total, which would put that total past 2551. So there's no way to that 2509 would be a perfect square. This logic can be used to eliminate the other wrong answers as well (with varying degrees of "necessary" math).

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

Thanks for the explanation. For the following similar question:

https://www.beatthegmat.com/which-of-the ... tml#717386

do we still use the same approach?

Thanks a lot,
Sri

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Jun 28, 2014 1:05 pm

Hi Sri,

The question that you linked (below), uses a different set of Number Properties and can be solved with a bit of brute-force calculations. My approach follows the question:

-----------------
Which of the following numbers is a perfect square?

A) 1266

B) 1444

C) 2022

D) 4034

E) 8122

OA: B
--------------

The first Number Property is that "perfect" squares can only end in certain digits: 1, 4, 5, 6, or 9. So the answers that end in "2" are not possible. Eliminate C and E.

From here, we just have to find the ONE ANSWER that's a perfect square. I'm going to focus on the first 2 answers, since they're "relatively close" to one another. If neither of them are perfect squares, then the answer would have to be D.

30^2 = 900
40^2 = 1600

Both A and are in that range (between 30 and 40), so we just need to narrow down the options a bit more...

The only possible perfect squares that could end in a 4 or a 6 (in this range) are...

32, 34, 36, 38

By starting with one of the "middle" options, I might be able to save some time/work...

34^2 = 1156 .....this is too small to be either answer A or B. I can now eliminate "32" as a possibility as well.

36^2 = 1296 .....not a match for either A or B.

38^2 = 1444 .....this IS a match!!!

Final Answer: B

While there are other high-concept approaches to answering this question, the GMAT does not require you to know them. I ultimately answered this question by thinking a bit about how multiplication "works" and then multiplying a couple of 2-digit numbers together. There are certain questions in which "brute force" is a great way to get the job done (and I consider this to be one of them); look at all the information that you're given though - there might be a way to avoid some of the work. In this question, I didn't have to check every number between 30 and 40, I only needed to check 3 of them.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Sun Jun 29, 2014 4:57 am

30^2 = 900

therefore if 961 is a perfect square then it has to be 31^2 because on 31^2 near 900 has unit digit 1

Check and get the answer.

OR Factorize every number and find the number with even powers in Prime factorization form, which is a lengthy process.

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

by gmattesttaker2 » Sun Jun 29, 2014 4:27 pm

[email protected] wrote:Hi Sri,

The question that you linked (below), uses a different set of Number Properties and can be solved with a bit of brute-force calculations. My approach follows the question:

-----------------
Which of the following numbers is a perfect square?

A) 1266

B) 1444

C) 2022

D) 4034

E) 8122

OA: B
--------------

The first Number Property is that "perfect" squares can only end in certain digits: 1, 4, 5, 6, or 9. So the answers that end in "2" are not possible. Eliminate C and E.

From here, we just have to find the ONE ANSWER that's a perfect square. I'm going to focus on the first 2 answers, since they're "relatively close" to one another. If neither of them are perfect squares, then the answer would have to be D.

30^2 = 900
40^2 = 1600

Both A and are in that range (between 30 and 40), so we just need to narrow down the options a bit more...

The only possible perfect squares that could end in a 4 or a 6 (in this range) are...

32, 34, 36, 38

By starting with one of the "middle" options, I might be able to save some time/work...

34^2 = 1156 .....this is too small to be either answer A or B. I can now eliminate "32" as a possibility as well.

36^2 = 1296 .....not a match for either A or B.

38^2 = 1444 .....this IS a match!!!

Final Answer: B

While there are other high-concept approaches to answering this question, the GMAT does not require you to know them. I ultimately answered this question by thinking a bit about how multiplication "works" and then multiplying a couple of 2-digit numbers together. There are certain questions in which "brute force" is a great way to get the job done (and I consider this to be one of them); look at all the information that you're given though - there might be a way to avoid some of the work. In this question, I didn't have to check every number between 30 and 40, I only needed to check 3 of them.

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

Thank you very much for the detailed and excellent explanation.

Best Regards,
Sri

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unknown13: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Jun 04, 2009 12:01 am; Thanked: 1 times

by unknown13 » Sun Jun 29, 2014 9:50 pm

Hi
I got the answer as B but i think i took the lengthy method of checking the sq root of the number manually. it took me 1 min and if the answer 961 will be the last option then i might land up spending more than 2.5 mins....

thanks and regards
Deepak Rustagi

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Mon Jun 30, 2014 1:38 am

https://burningmath.blogspot.in/2013/09/ ... quare.html

The techniques mentioned here can sometimes be useful.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 21, 2019 10:31 am

gmattesttaker2 wrote:Hello,

For the following:

Which of the following is a perfect square?

A) 649
B) 961
C) 1664
D) 2509
E) 100000

Let's look at each answer choice.

A) 649

Since 25^2 = 625, and since 26^2 = 676, 649 is not a perfect square.

B) 961

Since 30^2 = 900 and since 31^2 = 961, 961 is a perfect square.

Answer: B

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