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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
Joined: 26 Dec 2018
Posts: 142
Location: India
If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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05 Jan 2019, 10:32
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Difficulty:

45% (medium)

Question Stats:

57% (01:12) correct 43% (01:33) wrong based on 35 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

Source: Nova GMAT
Difficulty Level: 650

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Manager
Joined: 01 May 2017
Posts: 82
Location: India
Re: If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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05 Jan 2019, 19:09
2
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
VP
Joined: 31 Oct 2013
Posts: 1429
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul  [#permalink]

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06 Jan 2019, 04:50
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.

GMAT experts always say that test takers see the answer choices first. here is the key .
Re: If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul   [#permalink] 06 Jan 2019, 04:50
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# If (a – b)(a + b) = 7 x 13, then which one of the following pairs coul

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