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If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 I.
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17 Mar 2021, 09:54
17 Mar 2021, 09:54
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If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
I. a/b < 1
III. ab < 1
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
I. a/b > 0
I. a/b < 1
III. ab < 1
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 I.
[#permalink]
17 Mar 2021, 17:04
17 Mar 2021, 17:04
GIVEN: 1 > 1 - ab > 0
Multiply all 3 sides by -1 to get: -1 < -1 + ab < 0 [since I multiplied by a NEGATIVE number, I had to REVERSE the inequality symbols]
Add 1 to all 3 sides to get: 0 < ab < 1
First, if 0 < ab, then a and b are the SAME SIGN, which means a/b > 0
So, statement I is TRUE
ELIMINATE B and C
Second, our new inequality clearly tells us that ab < 1
So, statement III is TRUE
ELIMINATE A and D
So, we need not even check whether statement II is true.
Answer: E
Multiply all 3 sides by -1 to get: -1 < -1 + ab < 0 [since I multiplied by a NEGATIVE number, I had to REVERSE the inequality symbols]
Add 1 to all 3 sides to get: 0 < ab < 1
First, if 0 < ab, then a and b are the SAME SIGN, which means a/b > 0
So, statement I is TRUE
ELIMINATE B and C
Second, our new inequality clearly tells us that ab < 1
So, statement III is TRUE
ELIMINATE A and D
So, we need not even check whether statement II is true.
Answer: E
Re: If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 I.
[#permalink]
09 Apr 2022, 18:42
09 Apr 2022, 18:42
Assume : AB = 0.5 or 1/2
I. a/b > 0 ==> 2 / 0.25 = 8 > 0 TRUE
II. a/b < 1 ==> 8 < 1 NOT TRUE
III. ab < 1 ==> 1/2 < 1 TRUE
I. a/b > 0 ==> 2 / 0.25 = 8 > 0 TRUE
II. a/b < 1 ==> 8 < 1 NOT TRUE
III. ab < 1 ==> 1/2 < 1 TRUE
