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If p,q and r are positive numbers, does q lie between p and r on the

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If p,q and r are positive numbers, does q lie between p and r on the [#permalink]

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New post 21 Sep 2017, 00:25
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Difficulty:

  65% (hard)

Question Stats:

36% (01:43) correct 64% (01:37) wrong based on 25 sessions

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If p,q and R are positive numbers, does q lie between p and r on the number line?

1. 2p < q < 3r
2. 3r < 2q < 5p

Source : Experts Global

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If p,q and r are positive numbers, does q lie between p and r on the [#permalink]

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New post 21 Sep 2017, 03:14
pushpitkc wrote:
If p,q and R are positive numbers, does q lie between p and r on the number line?

1. 2p < q < 3r
2. 3r < 2q < 5p

Source : Experts Global


Given: p > 0, q > 0, r > 0
Question: Does q lie between p and r: p < q < r or r < q < p?

Statement 1:
2p < q < 3r
Since, 2p < q => p < q
q < 3r but it is not sufficient to know whether q < r because both q < r and q > r can be possible. For example, (q = 4, r = 5) and (q = 6, r = 3)
If q < r, then q lies between p and r and the answer is Yes, if q > r, then q does not lie between p and q and the answer is No.
Since p < q but q < r or q > r, statement 1 is not sufficient.

Statement 2:
3r < 2q < 5p
3r < 2q
q > 1.5r => q > r
2q < 5p => q < 2.5p
r < q < 2.5p
But, it is not enough to show whether r < q < p (which gives an answer Yes) or r, p < q (which gives an answer No)
So, statement 2 is not sufficient

Combining statements 1 and 2:
p < q and r < q
Since q is greater than both p and r, it does not lie between them. Since this information is enough to answer the question, both statements combined are sufficient.

Answer is C.
If p,q and r are positive numbers, does q lie between p and r on the   [#permalink] 21 Sep 2017, 03:14
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