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# If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =

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Math Expert
Joined: 02 Sep 2009
Posts: 54401
If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =  [#permalink]

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09 Apr 2019, 23:01
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:28) correct 24% (01:45) wrong based on 21 sessions

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If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =

(A) 2
(B) 4
(C) 8
(D) $$2 \sqrt{2}$$
(E) $$2 \sqrt{6}$$

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Manager
Joined: 17 May 2018
Posts: 69
Re: If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =  [#permalink]

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09 Apr 2019, 23:18
Subtract eqn2 from eqn2
Get 2q^2=8
Hence q=2
IMO A

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Joined: 18 Aug 2017
Posts: 3008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =  [#permalink]

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10 Apr 2019, 01:57
Bunuel wrote:
If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =

(A) 2
(B) 4
(C) 8
(D) $$2 \sqrt{2}$$
(E) $$2 \sqrt{6}$$

subtract p^2 - q^2 = 8 from p^2 + q^2 = 16
we get
q= 2
IMO A
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Intern
Joined: 11 Jan 2017
Posts: 6
Location: India
Re: If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =  [#permalink]

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10 Apr 2019, 03:36
p^2+q^2=16
p^2=16-q^2

p^2-q^2=8
16-q^2-q^2=8
q=2

IMO A
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Re: If p and q are positive, p^2 + q^2 = 16, and p^2 - q^2 = 8, then q =   [#permalink] 10 Apr 2019, 03:36
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