(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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sum of the squares of two integers_Kaplan
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conquistador
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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.
(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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GMATGuruNY
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Make a list of perfect squares up to 144: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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Brent@GMATPrepNow
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Here's a related question to practice with - https://www.beatthegmat.com/the-number-7 ... 74674.html
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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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
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
