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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If p and q are positive integers, and p < q, then which of
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26 May 2017, 13:28
26 May 2017, 13:28
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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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If p and q are positive integers, and p < q, then which of
[#permalink]
29 May 2017, 16:43
29 May 2017, 16:43
1
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
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:
Show: ::
B
Re: If p and q are positive integers, and p < q, then which of
[#permalink]
17 Feb 2022, 00:47
17 Feb 2022, 00:47
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
