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

Question

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

AC07 · Answer

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 .

saurabh9gupta · Answer

Bunuel  is there a way to solve this question algebraically?

chetan2u · Answer

All are POSITIVE and we have to find if q lies between p and r.. 1. 2p < q < 3r.. Find relationship between two of the variable.. (a) q>2p and 2p>p as p is positive...q>2p>p or q>p (b) 3r>q.... r>\frac{q}{3} ... If \frac{q}{3}q....ans is YES We can just be sure that q>p, no other relationship can be confirmed.. 2. 3r < 2q < 5p (a) 3r<2q..... q>\frac{3r}{2} and \frac{3r}{2}>r as r is positive... q>\frac{3r}{2}>r or q>r (b) 5p>2q.... p>\frac{2q}{5} ... If \frac{2q}{5}q....ans is YES We can just be sure that q>r, no other relationship can be confirmed.. Combined .. q>p and q>r, So answer is NO

Kinshook · Answer

Asked: If p,q and R are positive numbers, does q lie between p and r on the number line? 1. 2p < q < 3r p<2pr It is not clear whether q

p 2. 3r < 2q < 5p 2r<3r<2q<5p q>r Since q is greater than p & r, it doesn't lie between them on the number line IMO C

stne · Answer

hi  chetan2u ,  Kinshook  
 I am having difficulty combining the two statements to arrive at the final result that q > both p and r . Can you help.

Kinshook · Answer

stne

Please take each statement individually to arrive at q>p & q>r separately. There is no need to combine
Since q>p & q>r, p does not lie between them

{p,r}.........q

On the number line p & r lies on the same side of q. Therefore, q does not lie between p & r.

stne · Answer

Hi  Kinshook , 
Thank you for your reply , since same signs can be added in an inequality , can we not proceed in that manner?

Akp880 · Answer

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

Show Answer

Official Answer

C

Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.

For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum

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