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If r < 0 and 0 <pq/r < 1, which of
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10 Sep 2023, 10:04
10 Sep 2023, 10:04
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Question Stats:
37% (01:09) correct
62% (01:28) wrong based on 37 sessions
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If \(r < 0\) and \(0 <\frac{pq}{r }< 1\), which of the following must be true?
Indicate all that apply
A. p < 0
B. q < 0
C. p > q
D. p < q
E. pq > 0
F. pq < 0
G. pq < r
H. pq > r
Indicate all that apply
A. p < 0
B. q < 0
C. p > q
D. p < q
E. pq > 0
F. pq < 0
G. pq < r
H. pq > r
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Free Materials for the GRE General Exam - Where to get it!!
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: If r < 0 and 0 <pq/r < 1, which of
[#permalink]
10 Sep 2023, 11:51
10 Sep 2023, 11:51
Carcass can you please explain why H is correct ?
Re: If r < 0 and 0 <pq/r < 1, which of
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10 Sep 2023, 13:38
10 Sep 2023, 13:38
Expert Reply
Given that r < 0 and 0 < \(\frac{pq}{r}\) < 1 and we need to find which of the following is true
0 < \(\frac{pq}{r}\)
=> \(\frac{pq}{r}\) > 0
As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get
=> pq< r*0
=> pq < 0
\(\frac{pq}{r}\) < 1
As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get
=> pq > r
There is no other way to prove other options correct for sure
pq < 0
=> Either p > 0, q < 0 or p < 0, q > 0
But we cannot say for sure if any other option choice will be true.
So, Answer will be F, H
0 < \(\frac{pq}{r}\)
=> \(\frac{pq}{r}\) > 0
As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get
=> pq< r*0
=> pq < 0
\(\frac{pq}{r}\) < 1
As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get
=> pq > r
There is no other way to prove other options correct for sure
pq < 0
=> Either p > 0, q < 0 or p < 0, q > 0
But we cannot say for sure if any other option choice will be true.
So, Answer will be F, H
