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Difficulty:
15%
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Question Stats:
88% (01:03) correct
12%
(01:04)
wrong
based on 57
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If p, q are each greater than 0 but less than 1, which of the following may be true?
I. p / q > 1
II. pq > 1
III. q – p > 1
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
I. p / q > 1
II. pq > 1
III. q – p > 1
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
BongBideshini
Joined: 25 May 2021
Last visit: 22 Apr 2026
Posts: 136
Given Kudos: 78
Location: India
Concentration: Entrepreneurship, Marketing
Schools: HBS '27 Stanford '27 Wharton '27 Sloan '27
GPA: 3.8
WE:Engineering (Government)
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17 Apr 2026, 11:13
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I. p/q>1
Example: p=0.8, q=0.4 gives 0.8/0.4=2
So I may be true.
II. pq>1
0<p<1
0<q<1
Using the inequality multiplication property, we can write
0<pq<1
So II cannot be true.
III. q−p>1
Both p and q must lie between 0 and 1 on the number line.
If q > p,
0 ..... p ..... q ..... 1
Then q − p represents the distance between q and p
Since both numbers are inside the interval from 0 to 1, that distance must be less than 1
So:
q − p < 1
If p > q,
0 ..... q ..... p ..... 1
Then,
q − p < 0
So in either case, q − p can never be greater than 1.
Therefore, Statement III cannot be true.
Ans A
Example: p=0.8, q=0.4 gives 0.8/0.4=2
So I may be true.
II. pq>1
0<p<1
0<q<1
Using the inequality multiplication property, we can write
0<pq<1
So II cannot be true.
III. q−p>1
Both p and q must lie between 0 and 1 on the number line.
If q > p,
0 ..... p ..... q ..... 1
Then q − p represents the distance between q and p
Since both numbers are inside the interval from 0 to 1, that distance must be less than 1
So:
q − p < 1
If p > q,
0 ..... q ..... p ..... 1
Then,
q − p < 0
So in either case, q − p can never be greater than 1.
Therefore, Statement III cannot be true.
Ans A
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