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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 [#permalink]

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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 30 Jan 2018, 00:36
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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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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 30 Jan 2018, 01:59
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Bunuel wrote:
Which of the following is NOT a difference between two perfect squares?

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


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
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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 31 Jan 2018, 17:08
Bunuel wrote:
Which of the following is NOT a difference between two perfect squares?

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


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
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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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

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



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
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Which of the following is NOT a difference between two perfect squares [#permalink]

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New post Updated on: 01 Feb 2018, 00:08
Bunuel wrote:
Which of the following is NOT a difference between two perfect squares?

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


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. \((a+b)(a-b) = (5\sqrt{2} + 4\sqrt{2})(5\sqrt{2}-4\sqrt{2}) = 18\)
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Originally posted by rahul16singh28 on 31 Jan 2018, 20:08.
Last edited by rahul16singh28 on 01 Feb 2018, 00:08, edited 1 time in total.
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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 01 Feb 2018, 00:00
\((5\sqrt{2})^2\)= 50 [Not a perfect square]
\((4\sqrt{2})^2\)= 32 [Not a perfect square]
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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 01 Feb 2018, 00:06
varun4s wrote:
\((5\sqrt{2})^2\)= 50 [Not a perfect square]
\((4\sqrt{2})^2\)= 32 [Not a perfect square]

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.. !!

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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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rahul16singh28 wrote:
varun4s wrote:
\((5\sqrt{2})^2\)= 50 [Not a perfect square]
\((4\sqrt{2})^2\)= 32 [Not a perfect square]

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.. !!

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A perfect square is a square of an integer.
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Re: Which of the following is NOT a difference between two perfect squares [#permalink]

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New post 01 Feb 2018, 00:32
rahul16singh28 wrote:
Bunuel wrote:
Which of the following is NOT a difference between two perfect squares?

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


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. \((a+b)(a-b) = (5\sqrt{2} + 4\sqrt{2})(5\sqrt{2}-4\sqrt{2}) = 18\)


Hi Rahul,
If we go by this EVERY number will be a perfect square..
But a perfect square means a square of an INTEGER
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Re: Which of the following is NOT a difference between two perfect squares   [#permalink] 01 Feb 2018, 00:32
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