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If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul

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Manager
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If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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New post 05 Jan 2019, 09:32
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

59% (00:56) correct 41% (01:36) wrong based on 29 sessions

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If (a – b)(a + b) = 7 x 13, then which one of the following pairs could be the values of a and b, respectively?

(A) 7, 13
(B) 5, 15
(C) 3, 10
(D) –10, 3
(E) –3, –10

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If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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New post 05 Jan 2019, 18:09
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If \((a – b)(a + b) = 7*13\), then which one of the following pairs could be the values of a and b, respectively?

In the above equation both a-b and a+b may result in positive or the negative values(cancel out the sign)
Since 7,13 are prime we can consider a-b = 7, a+b = 13 OR a-b = -7 and a+b = -13 OR a-b = -13 , a+b = -7 ....So many possibilities

Better
We can go with option verification,
Only option D satisfies,
Option D implies,
\(a+b = -10+3 = -7\)
\(a-b = -10-3 = -13\)
satisfying the condition \((a-b)(a+b) = 7*13\)
Option D is correct
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If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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New post 06 Jan 2019, 03:50
UB001 wrote:
If (a – b)(a + b) = 7 x 13, then which one of the following pairs could be the values of a and b, respectively?

(A) 7, 13
(B) 5, 15
(C) 3, 10
(D) –10, 3
(E) –3, –10


\((a-b)(a+b) = a^2 -b^2\)

\(a^2 -b^2 = 7*13\)

\(a^2 - b^2 =91.\)

\((-10)^2 -(3)^2 = 91\)

Thus correct answer is D.

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If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul &nbs [#permalink] 06 Jan 2019, 03:50
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