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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]  09 May 2015, 11:25
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Question Stats:

69% (00:46) correct 30% (00:52) wrong based on 81 sessions
$$p + q = 1$$
$$0 < p < q$$

 Quantity A Quantity B $$\frac{1}{pq}$$ $$1$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Last edited by Carcass on 20 Feb 2020, 11:13, edited 1 time in total.
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Re: GRE Math Challenge #107 [#permalink]  12 May 2015, 07:39
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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

[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]  11 Aug 2018, 13:01
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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.

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Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q [#permalink]  20 Feb 2020, 11:14
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Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q [#permalink]  21 Feb 2020, 08:51
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I'm making this question complicated just to add another discussion point.

0<p<q
p+q = 1

So, p = 1- q

Now 0< 1-q < q (replaced p with 1-q)

0<1-q or 1-q<q
So q<1 or q>1/2

Therefore q can be 3/4 and p can be 1/4

3/4 times 1/4 = 3/16

1/(3/16) = 16/3 or 5.33 . Therefore A is greater than B
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Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q [#permalink]  24 Feb 2020, 01:57
Thank you
Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q   [#permalink] 24 Feb 2020, 01:57
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