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If a + (1/b) = 400, and a < -300, then which of the following must be

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If a + (1/b) = 400, and a < -300, then which of the following must be [#permalink] New post   18 Mar 2021, 10:17
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If a + (1/b) = 400, and a < -300, then which of the following must be true?

A) b > -700
B) b > 1/(-100)
C) b > 1/ 300
D) b > 700
E) b < 1/700


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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E
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Re: If a + (1/b) = 400, and a < -300, then which of the following must be [#permalink] New post   18 Mar 2021, 10:35
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Carcass wrote:
If a + (1/b) = 400, and a < -300, then which of the following must be true?

A) b > -700
B) b > 1/(-100)
C) b > 1/ 300
D) b > 700
E) b < 1/700


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


Given: a + (1/b) = 400
Subtract 1/b from both sides to get: a = 400 - 1/b

Also given: a < -300
Replace a with 400 - 1/b to get: 400 - 1/b < -300
Add 1/b to both sides: 400 < -300 + 1/b
Add 300 to both sides: 700 < 1/b

IMPORTANT: 700 < 1/b, then b must be POSITIVE
Since b is POSITIVE, we can safely multiply both sides of the inequality by b to get: 700b < 1
Finally, divide both sides by 700 to get: b < 1/700

Answer: E
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Re: If a + (1/b) = 400, and a < -300, then which of the following must be [#permalink] New post   13 Apr 2023, 06:52
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a + (1/b) = 400, and a < -300, then which of the following must be [#permalink]
13 Apr 2023, 06:52
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