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sum of the squares of two integers_Kaplan

by conquistador » Sat Nov 21, 2015 2:57 am
Which of the following is NOT the sum of the squares of two integers?

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

I spent nearly 4 minutes and selected a wrong choice. While we know how to solve this problem by normal hard working process , I request someone to share if they can smartly solve the problem with some logic. :)
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by GMATGuruNY » Sat Nov 21, 2015 3:22 am
Mechmeera 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
Make a list of perfect squares up to 144:
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

Prove that four of the five answer choices CAN be written as the sum of two values from the list above:
A: 36 = 0 + 36
B: 37 = 1 + 36
C: 65 = 1 + 64
D: 146 = 25 + 121

The correct answer is E.
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by Brent@GMATPrepNow » Sat Nov 21, 2015 11:37 am
Here's a related question to practice with - https://www.beatthegmat.com/the-number-7 ... 74674.html

Cheers,
Brent
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by [email protected] » Sat Nov 21, 2015 11:59 am
Hi Mechmeera,

Mitch's approach is spot-on, so I won't rehash any of that work here. 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 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), so the real work involves figuring out whether Answer D or E is the one that that you cannot get to.

If you start with 144, there's 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 have the correct answer.

Final Answer: E

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by Matt@VeritasPrep » Fri Nov 27, 2015 2:47 am
The hint seems to be how close the first few answers are to friendly squares.

36 = 6*6 + 0*0
37 = 6*6 + 1*1
65 = 8*8 + 1*1

From there, I went to 144 + x = 146 or 147, but that didn't give any squares, so I dropped to the previous square, 121. 121 + 25 gave 146, and that was that!

Hard to go wrong in assuming the question writers are lazy, in my experience :)
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