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GRE Math Challenge #107- p + q = 1 and 0 < p < q
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Updated on: 26 Jan 2022, 14:33
Updated on: 26 Jan 2022, 14:33
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79% (01:00) correct
20% (01:07) wrong based on 144 sessions
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\(p + q = 1\)
\(0 < p < q\)
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.
Kudos for the right answer and explanation
\(0 < p < q\)
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.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q
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12 May 2015, 07:39
12 May 2015, 07:39
1
sandy wrote:
\(p + q = 1\)
\(0 < p < q\)
Quantity A: \(1/pq\)
Quantity B: 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:
Show: ::
A
Cheers,
Brent
Re: GRE Math Challenge #107- p + q = 1 and 0 < p < q
[#permalink]
11 Aug 2018, 13:01
11 Aug 2018, 13:01
1
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
\(0 < p < q\)
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.
