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GRE Math Challenge #107- p + q = 1 and 0 < p < q

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GRE Math Challenge #107- p + q = 1 and 0 < p < q [#permalink] New post 09 May 2015, 11:25
Expert's post
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Question Stats:

62% (00:27) correct 37% (01:38) wrong based on 8 sessions
\(p + q = 1\)
\(0 < p < q\)

Quantity A: \(1/pq\)
Quantity B: 1
• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #107 [#permalink] New post 12 May 2015, 07:39
Expert's post
sandy wrote:
\(p + q = 1\)
\(0 < p < q\)

Quantity A: \(1/pq\)
Quantity B: 1


Two important facts:
1) since p and q are both positive, the product pq is POSITIVE
2) since p and q are both positive, AND p + q = 1, we can conclude that p and q are each less than 1

The fraction in quantity A might cause issues for us, so let's eliminate that fraction.
Since fact #1 tells us that the product pq is POSITIVE, let's multiply both quantities by pg to get:
Quantity A: 1
Quantity B: pq

Next, since p and q are each less than 1, the product pq must be less than 1.
So, we get:
Quantity A: 1
Quantity B: some number less than 1


Answer:
[Reveal] Spoiler:
A


Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q [#permalink] New post 11 Aug 2018, 13:01
sandy wrote:
\(p + q = 1\)
\(0 < p < q\)

Quantity A: \(1/pq\)
Quantity B: 1
• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined



p + q = 1

and 0<p<q.

From the given data , it's clear that both p ans q are positive fraction.

When we divide an integer by a fraction , the integer becomes much bigger. So, 1 will be greater than before.

The best answer is A.
Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q   [#permalink] 11 Aug 2018, 13:01
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GRE Math Challenge #107- p + q = 1 and 0 < p < q

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