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If p and q are positive integers, and p < q, then which of

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GRE Instructor
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Joined: 10 Apr 2015
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If p and q are positive integers, and p < q, then which of [#permalink] New post 26 May 2017, 13:28
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62% (01:10) correct 37% (02:09) wrong based on 16 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

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GRE Instructor
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Joined: 10 Apr 2015
Posts: 1228
Followers: 45

Kudos [?]: 1105 [0], given: 7

Re: If p and q are positive integers, and p < q, then which of [#permalink] New post 29 May 2017, 16:43
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

Answer:
[Reveal] Spoiler:
B

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Re: If p and q are positive integers, and p < q, then which of   [#permalink] 29 May 2017, 16:43
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If p and q are positive integers, and p < q, then which of

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