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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. If p and q are positive integers, and p < q, then which of  Question banks Downloads My Bookmarks Reviews Important topics
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GRE Instructor Joined: 10 Apr 2015
Posts: 1971
Followers: 60

Kudos [?]: 1798 , given: 9

If p and q are positive integers, and p < q, then which of [#permalink]
Expert's post 00:00

Question Stats: 65% (01:33) correct 34% (02:02) wrong based on 26 sessions
If p and q are positive integers, and p < q, then which of the following MUST be true?

I) p/q < (p+1)/(q+1)

II) (p–1)/q < (p+1)/q

III) (p–1)/q < (p–1)/(p+1)

A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com GRE Instructor Joined: 10 Apr 2015
Posts: 1971
Followers: 60

Kudos [?]: 1798 , given: 9

Re: If p and q are positive integers, and p < q, then which of [#permalink]
Expert's post
GreenlightTestPrep wrote:
If p and q are positive integers, and p < q, then which of the following MUST be true?

I) p/q < (p+1)/(q+1)

II) (p–1)/q < (p+1)/q

III) (p–1)/q < (p–1)/(p+1)

A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Statement I: There's a nice rule that says "If we add the same positive value to the numerator and denominator of a positive fraction, the resulting fraction is closer to one than the original fraction was.
For example (23+8)/(50+8) is closer to 1 than is 23/50

Since p < q, we know that p/q is less than 1
By the above rule, we know that (p+1)/(q+1) is closer to 1 than is p/q, which means p/q < (p+1)/(q+1) < 1
Statement I is TRUE

Statement II: The positive denominators are the same, but the numerator p+1 is greater than p-1
So, it must be the case that (p-1)/q < (p+1)/q
Statement II is TRUE

Statement III: This time the numerators are the same, but the denominators are different (q and p+1)
We can right away that if p = 1, then the two sides are EQUAL
In other words, it is NOT the case that (p–1)/q < (p–1)/(p+1)
Statement III need NOT be true

[Reveal] Spoiler:
B

_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: If p and q are positive integers, and p < q, then which of   [#permalink] 29 May 2017, 16:43
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