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If a and b are non-zero integers and ab >b, which of the following mus
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18 Nov 2021, 04:12
18 Nov 2021, 04:12
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If a and b are non-zero integers and ab >b, which of the following must be true?
I. a/b > 0
II. (a - b) > 0
II. (a + b) > 1
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
GRE Tips and Tricks - UPDATED 11/15/2021
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
I. a/b > 0
II. (a - b) > 0
II. (a + b) > 1
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
GRE Tips and Tricks - UPDATED 11/15/2021
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
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Given Kudos: 9
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Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: If a and b are non-zero integers and ab >b, which of the following mus
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18 Nov 2021, 04:52
18 Nov 2021, 04:52
1
We are given that a and b are non-zero integers and ab >b
=> ab - b > 0 => b (a-1) > 0. There will be two cases
Case 1: Either both b and a-1 are positive
=> b > 0 and a-1 > 0
=> b > 0 and a > 1
I. a/b > 0
TRUE as both a and b are positive so a/b > 0
II. (a - b) > 0
a-b > 0, Not necessary as b can be 3 and a can be 2
III. (a + b) > 1
a + b > 1 is TRUE
as a> 1 and b> 0
Case 2: Both b and a-1 are negative
=>b < 0 and a-1 < 0
=> b < 0 and a < 1
Since, a is a non-zero integer
=> a < 0 and b < 0
I. a/b > 0
TRUE as both a and b are negative so a/b > 0
II. (a - b) > 0
a-b > 0, Not necessary as a can be -3 and b can be -2
making a-b = (-3) - (-2) = -1 which is < 0
III. (a + b) > 1
a + b > 1 is FALSE
As both a and b are negative
Combining both the cases the only option which is true in both of them is Option I
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Inequalities
=> ab - b > 0 => b (a-1) > 0. There will be two cases
Case 1: Either both b and a-1 are positive
=> b > 0 and a-1 > 0
=> b > 0 and a > 1
I. a/b > 0
TRUE as both a and b are positive so a/b > 0
II. (a - b) > 0
a-b > 0, Not necessary as b can be 3 and a can be 2
III. (a + b) > 1
a + b > 1 is TRUE
as a> 1 and b> 0
Case 2: Both b and a-1 are negative
=>b < 0 and a-1 < 0
=> b < 0 and a < 1
Since, a is a non-zero integer
=> a < 0 and b < 0
I. a/b > 0
TRUE as both a and b are negative so a/b > 0
II. (a - b) > 0
a-b > 0, Not necessary as a can be -3 and b can be -2
making a-b = (-3) - (-2) = -1 which is < 0
III. (a + b) > 1
a + b > 1 is FALSE
As both a and b are negative
Combining both the cases the only option which is true in both of them is Option I
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Inequalities
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Joined: 10 Apr 2015
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Given Kudos: 136
If a and b are non-zero integers and ab >b, which of the following mus
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18 Nov 2021, 06:16
18 Nov 2021, 06:16
1
Carcass wrote:
If a and b are non-zero integers and ab >b, which of the following must be true?
I. a/b > 0
II. (a - b) > 0
II. (a + b) > 1
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. a/b > 0
II. (a - b) > 0
II. (a + b) > 1
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Let's test some possible values of a and b...
If ab >b, then it could be the case that a = -2 and b = -1
Now plug these values into each of the statements....
I. (-2)/(-1) > 0. TRUE!
II. (-2) - (-1) > 0. NOT TRUE
II. (-2) + (-1) > 1. NOT TRUE
At this point, we can eliminate all answer choices except for A.
Answer: A
