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

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Jul 30, 2018 10:49 pm

BTGmoderatorDC 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

This does not seem to be a genuine GMAT-like question. The first three options are easier ones, but the last two needs a hit and trail work. Anyways, here's the solution.

(A) 36 = 0^2 + 6^2: possible
(B) 37 = 1^2 + 6^2: possible
(C) 65 = 1^2 + 8^2: possible
(D) 146 = 5^2 + 11^2: possible
(E) 147 = Since 146 is possible, the very next number 147 is not possible.

The correct answer: E

Hope this helps!

-Jay
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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] » Mon Aug 06, 2018 7:42 pm

Hi All,

Which of the following is NOT the sum of the squares of two integers. This question has a great 'brute force' approach to it. 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: E

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

Contact Rich at [email protected]

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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 Aug 10, 2018 5:53 pm

BTGmoderatorDC 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]