Which of the following is NOT a difference between two perfect squares

Question

Which of the following is NOT a difference between two perfect squares?

A. 5
B. 7
C. 8
D. 13
E. 18

Kurtosis · Answer

A. 3^2 - 2^2 = 5

B. 4^2 - 3^2 = 7

C. 3^2 - 1^2 = 8

D. 7^2 - 6^2 = 13

Answer: E

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GMATinsight · Answer

difference between two perfect squares = a^2 - b^2 = (a+b)*(a-b)

Hence the number which can not be represented in form of (a+b)*(a-b) form will be our answer

Also, every odd number can be represented in (a+b)*(a-b) form (as shown in calculation below)  hence options A,B and E are straight out

A. 5 = 5*1 = (3+2)*(3-2)
B. 7 = 7*1 = (4+3)*(4-3)
C. 8 = 4*2 = (3+1)*(3-1)
D. 13 = 13*1 = (7+6)*(7-6)
E. 18 CAN'T be represented as (a+b)*(a-b) form

Answer: option B

ScottTargetTestPrep · Answer

The first few perfect squares are 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36, and 7^2 = 49. Let’s test our answer choices:

A) 5

9 - 4 = 5

B) 7

16 - 9 = 7

C) 8

9 - 1 = 8

D) 13

49 - 36 = 13

E) 18

We see that 18 cannot be the difference between 2 perfect squares.

Answer: E

chetan2u · Answer

There is always logic in almost all Questions..

So what is the point here..
 a^2-b^2=(a-b)(a+b) ..
If a-b is even, a+b will be even and if a-b is odd, a+b will be odd...
So if a number cannot be written as O*O or E*E, that is our answer..
1) 5=1*5..o*o
2) 7=1*7..o*o
3) 8=2*4..E*E
4) 13= 1*13..o*o
5) 18=1*18=2*9=3*6...o*E.. thus our ANSWER..

E

rahul16singh28 · Answer

Hi  Bunuel

I think the question is missing something here.. because all the options are difference between two perfect square  NUMBERS .

chetan2u  Can you please let me know if I am missing anything here.

A.  (a+b)(a-b) = (3+2)(3-2) = 5 
B.  (a+b)(a-b) = (4+3)(4-3) = 7 
C.  (a+b)(a-b) = (3+1)(3-1) = 8 
D.  (a+b)(a-b) = (7+6)(7-6) = 13 
E.  (a+b)(a-b) = (5\sqrt{2} + 4\sqrt{2})(5\sqrt{2}-4\sqrt{2}) = 18

varun4s · Answer

(5\sqrt{2})^2 = 50  
 (4\sqrt{2})^2 = 32

rahul16singh28 · Answer

They are perfect squares.. 50 = (5√2)^2 and 32 = (4√2)^2... Also, it's not mentioned in the question that whether it's a integer or a Number.. !!

Sent from my Lenovo P1a42 using  GMAT Club Forum mobile app

Bunuel · Answer

A perfect square is a square of an integer.

chetan2u · Answer

Hi Rahul,
If we go by this EVERY number will be a perfect square..
But a perfect square means a square of an INTEGER

exc4libur · Answer

a^2-b^2=(a+b)(a-b)
(a+b)(a-b)=5: (a+b=5)(a-b=1)… 2a=6, a=3 b=2 valid
(a+b)(a-b)=7: 7*1… 2a=8, a=4 b=3 valid
(a+b)(a-b)=8: 4*2… 2a=6, a=3 b=3 valid
(a+b)(a-b)=13: 13*1… 2a=14, a=7 b=6 valid

(a+b)(a-b)=18: (a+b=18)(a-b=1)…2a=19, a≠integer
(a+b)(a-b)=18: (a+b=9)(a-b=2)…2a=11, a≠integer
(a+b)(a-b)=18: (a+b=6)(a-b=3)…2a=9, a≠integer

Ans (E)

GMATBusters · Answer

Difference of 2 perfect Sqaures : a^2-b^2 = (a+b)(a+b)

Since,  a and b are both integers, either both (a+b) and (a-b) are even or both odd.

Hence, if  (a+b)(a+b) is even, it MUST be multiple of 4 . We cannot have (a+b)(a+b) even but NOT multiple of 4.

Clearly, from given options, 18 is even but NOT a multiple of 4, and hence is NOT a difference between two perfect squares.

E is the right answer.

Which of the following is NOT a difference between two perfect squares

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Which of the following is NOT a difference between two perfect squares

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