Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 22:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Which of the following is NOT the sum of the squares of two

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 409
Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

Updated on: 09 Jan 2014, 06:59
1
13
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:00) correct 42% (01:40) wrong based on 361 sessions

### HideShow timer Statistics

Which of the following is NOT the sum of the squares of two integers?

(A) 36
(B) 37
(C) 65
(D) 146
(E) 147

OE
NOTE: Zero = Integer
0^2 = 0; 1^2 = 1; 2^2 = 4; 3^2 = 9; 4^2 = 16; 5^2 = 25; 6^2 = 36; 7^2 = 49; 8^2 = 64; 9^2 = 81; 10^2 = 100; 11^2 = 121; 12^2 = 144

(A): 0^2 + 6^2 = 0 + 36 = 36
(B): 1^2 + 6^2 = 1 + 36 = 37
(C): 1^2 + 8^2 = 1 + 64 = 65
(D): 5^2 + 11^2 = 25 + 121 = 146

Hi, I can see how we can find the answer. I want to know the quick way to spot combinations of (square of) 2 integers, please.

Originally posted by goodyear2013 on 09 Jan 2014, 06:54.
Last edited by Bunuel on 09 Jan 2014, 06:59, edited 1 time in total.
Edited the question.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

09 Jan 2014, 10:42
goodyear2013 wrote:
Which of the following is NOT the sum of the squares of two integers?

(A) 36
(B) 37
(C) 65
(D) 146
(E) 147

Hi, I can see how we can find the answer. I want to know the quick way to spot combinations of (square of) 2 integers, please.

Dear goodyear2013,
I'm happy to respond.

I don't really like this question, and I don't consider it particularly GMAT-like. On a good GMAT math question, even a hard one, there's often some perspective that allows for a particularly elegant solution. With this problem, it's easy to eliminate the first three answers, but then we have to fish around for the combination that will add up to 146 or 147. There's no particularly quick way to do this. There is nothing especially elegant about this problem. That's why I don't like it. Don't worry; you are not missing some crucial mathematical trick.

Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern
Joined: 12 Sep 2012
Posts: 24
GMAT 1: 550 Q49 V17
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

16 May 2014, 08:50
Hi mikemcgarry,
Could you tell me why you are eliminating the first three choices. Your kind intervention is sought.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

16 May 2014, 18:23
1
deya wrote:
Hi mikemcgarry,
Could you tell me why you are eliminating the first three choices. Your kind intervention is sought.

Dear deya
I'm happy to respond.

We know that 6^2 = 36, so (6^2) + (0^2) = 36. (Remember, "integers" includes positive and negative and zero!!)

Then, notice that 37 = 36 + 1 = (6^2) + (1^2)
and that 65 = 64 + 1 = (8^2) + (1^2).

If you see those three things, it's easy to eliminate the first three.

Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Senior Manager
Joined: 28 Jun 2015
Posts: 272
Concentration: Finance
GPA: 3.5
Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

14 Jul 2015, 19:30
2
List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

(A) 36 - 9+25. NO.
(B) 37 - 1+36. NO.
(C) 65 - 1+64. NO.
(D) 146 - 25+121. NO.
(E) - must be the answer.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Board of Directors
Joined: 17 Jul 2014
Posts: 2429
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

13 Jan 2016, 18:19
easy one, need 47 seconds to get to the answer:
(A) 36 = 25+9 or 5^2 + 3^2
(B) 37 = 36+1 or 6^2 + 1^2
(C) 65 = 49+16 or 7^2 + 4^2
(D) 146 = 121+25 or 11^2+5^2
(E) 147 - by POE, we are left with E.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

14 Jan 2016, 10:27
1
FireStorm wrote:
List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
(A) 36 - 9+25. NO.

mvictor wrote:
easy one, need 47 seconds to get to the answer:
(A) 36 = 25+9 or 5^2 + 3^2

Dear FireStorm & mvictor,
My friends, at the risk of pointing out the obvious, 25 + 9 = 34, not 36.

Getting 36 as a sum requires remembering that zero is, in fact, an integer. Therefore, 6^2 + 0^2 = 36, a sum of the squares of integers.

My friends, never underestimate simple arithmetic. The kind of mindfulness that can keep track of each simple arithmetic on the GMAT Quant might account for a 50+ point difference in score.

Best of luck, my friends!
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16797
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

12 Feb 2018, 12:00
Hi All,

This question has a great 'brute force' approach. Sometimes the big 'shortcut' that you'll find in a prompt is in the way that you organize your information. For this question, try writing the first 12 perfect squares VERTICALLY (instead of horizontally):

0
1
4
9
16
25
36
49
64
81
100
121
144

Looking at the numbers in this way, you can focus on the UNITS DIGITS, so it should be easier/faster to find the 4 answer choices that ARE the sum of perfect squares and the 1 that is NOT.

The first 3 answers are relatively small (and easy to spot):
36 = 0 + 36
37 = 1 + 36
65 = 1 + 64

The real work involves figuring out whether Answer D or E is the one that that you cannot get to.

If you start with the biggest number first - in this case, 144 - then there's clearly no number in the list that will get you to 146 or 147.

Next, try the 121....whatever you add to this number would need to have a 5 or a 6 as a units digit....25 is the match. Thus, you know that 146 IS possible while 147 must be the one that's not.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10683
Location: United States (CA)
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

10 Aug 2018, 18:01
goodyear2013 wrote:
Which of the following is NOT the sum of the squares of two integers?

(A) 36
(B) 37
(C) 65
(D) 146
(E) 147

We can check each given answer choice to see whether it can be expressed as a sum of two squares.

(A) 36 = 6^2 + 0^2

(B) 37 = 6^2 + 1^2

(C) 65 = 8^2 + 1^2

(D) 146 = 11^2 + 5^2

Thus, we see that 147 in choice E is the only number that cannot be expressed as a sum of two squares.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 15110
Re: Which of the following is NOT the sum of the squares of two  [#permalink]

### Show Tags

07 Mar 2020, 05:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Which of the following is NOT the sum of the squares of two   [#permalink] 07 Mar 2020, 05:38