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# If p + q = 3 and p – q = 17, then pq =

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
If p + q = 3 and p – q = 17, then pq =  [#permalink]

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22 Jul 2019, 00:53
00:00

Difficulty:

15% (low)

Question Stats:

83% (00:44) correct 17% (01:06) wrong based on 52 sessions

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If p + q = 3 and p – q = 17, then pq =

A. -70
B. -60
C. 0
D. 10
E. 70

_________________
VP
Joined: 31 Oct 2013
Posts: 1493
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If p + q = 3 and p – q = 17, then pq =  [#permalink]

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22 Jul 2019, 00:58
1
Bunuel wrote:
If p + q = 3 and p – q = 17, then pq =

A. -70
B. -60
C. 0
D. 10
E. 70

p + q = 3

p – q = 17

.........................
2p = 20

p = 10.

substitute this value:

p + q = 3

10 + q = 3

q = -7.

Required Value ;

pq

(10) ( -7) = -70.

SVP
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34
Re: If p + q = 3 and p – q = 17, then pq =  [#permalink]

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22 Jul 2019, 00:59
Bunuel wrote:
If p + q = 3 and p – q = 17, then pq =

A. -70
B. -60
C. 0
D. 10
E. 70

Given: p + q = 3 and p – q = 17,

q=-7

pq = 10*(-7) = -70

IMO A
Intern
Joined: 18 Jun 2017
Posts: 9
Location: India
Concentration: Sustainability, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: If p + q = 3 and p – q = 17, then pq =  [#permalink]

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02 Aug 2019, 08:05
$$(a+b)^2$$ - $$(a-b)^2$$ = 4xy

In this case,

$$(p+q)^2$$ - $$(p-q)^2$$ = 4pq

=> $$3^2$$ - $$17^2$$ = 4pq
=> 9 - 289 = 4pq
=> pq = -280/4 = -70
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9125
Location: United States (CA)
Re: If p + q = 3 and p – q = 17, then pq =  [#permalink]

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04 Aug 2019, 11:41
Bunuel wrote:
If p + q = 3 and p – q = 17, then pq =

A. -70
B. -60
C. 0
D. 10
E. 70

Adding the equations together, we have:

2p = 20

p = 10

So, q is:

10 + q = 3

q = -7

Thus, pq is -70.

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Re: If p + q = 3 and p – q = 17, then pq =   [#permalink] 04 Aug 2019, 11:41
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