Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jul 28 07:00 PM EDT  08:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Sunday, July 28th at 7 PM EDT
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 414

Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
Updated on: 09 Jan 2014, 07:59
Question Stats:
61% (02:01) correct 39% (01:41) wrong based on 433 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.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by goodyear2013 on 09 Jan 2014, 07:54.
Last edited by Bunuel on 09 Jan 2014, 07:59, edited 1 time in total.
Edited the question.



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4487

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
09 Jan 2014, 11:42
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 GMATlike. 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 PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Intern
Joined: 12 Sep 2012
Posts: 25

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
16 May 2014, 09:50
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: 4487

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
16 May 2014, 19:23
deya wrote: Hi mikemcgarry, Could you tell me why you are eliminating the first three choices. Your kind intervention is sought. Dear deyaI'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 PrepEducation 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: 286
Concentration: Finance
GPA: 3.5

Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
14 Jul 2015, 20:30
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: 2538
Location: United States (IL)
Concentration: Finance, Economics
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, 19:19
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: 4487

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
14 Jan 2016, 11:27
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 PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14620
Location: United States (CA)

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
12 Feb 2018, 13:00
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. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6991
Location: United States (CA)

Re: Which of the following is NOT the sum of the squares of two
[#permalink]
Show Tags
10 Aug 2018, 19:01
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. Answer: E
_________________
5star 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.




Re: Which of the following is NOT the sum of the squares of two
[#permalink]
10 Aug 2018, 19:01






