If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?
A) root(p/q)
B) p/(p^2)
C) p/2q
D) q/(p^2)
E) q/p
Which must be greate than 1?
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 116
 Joined: 31 Mar 2009
 Followed by:1 members
 Patrick_GMATFix
 GMAT Instructor
 Posts: 1053
 Joined: 21 May 2010
 Thanked: 335 times
 Followed by:98 members
Since we're dealing with positive integers, we can cross multiply to find that p < q. As a result, q/p must be greater than 1 (answer E). The full solution below is taken from the GMATFix App. It discusses each answer choice in detail
Patrick
Patrick
 Check out my site: GMATFix.com
 To prep my students I use this tool >> (screenshots, video)
 Ask me about tutoring.
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15795
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1267 members
 GMAT Score:770
Given: p/q < 1LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?
A) âˆš(p/q)
B) p/(pÂ²)
C) p/2q
D) q/(pÂ²)
E) q/p
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q
Which of the following MUST be greater than 1?
IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty testmaker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.
E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.
A) âˆš(p/q)
Let p = 1 and q = 4 to get: âˆš(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A
B) p/(pÂ²)
Let p = 2 to get: 2/(2Â²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B
C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C
D) q/(pÂ²)
Let p = 1 and q = 2 to get: 2/(1Â²) = 4
4 IS greater than 1, so KEEP D
E) q/p
Let p = 1 and q = 2 to get: 2/1 = 2
2 IS greater than 1, so KEEP E
We have eliminated A, B, and C. So, we must try a DIFFERENT set of values for answer choices D and E.
D) q/(pÂ²)
Let p = 2 and q = 3 to get: 3/(2Â²) = 3/4
3/4 is NOT greater than 1, so ELIMINATE D
So, the correct answer must be E
Cheers,
Brent
Last edited by [email protected] on Tue Nov 17, 2015 10:50 am, edited 1 time in total.
 Abhishek009
 Master  Next Rank: 500 Posts
 Posts: 359
 Joined: 11 Mar 2009
 Location: Kolkata, India
 Thanked: 50 times
 Followed by:2 members
Plug in some valuesLulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?
A) root(p/q)
B) p/(p^2)
C) p/2q
D) q/(p^2)
E) q/p
p/q < 1 and p and q are positive integers
Let P = 2 and q = 3
p/q = 0.667 < 1
Now check each options matter of just 10 seconds 
A) root(p/q) root 2/3
B) p/(p^2)= 2/4
C) p/2q = 2/6
D) q/(p^2) = 3/4
E) q/p = 3/2 => 1.5 This is the answer...
IMO (E)
Abhishek
GMAT/MBA Expert
 [email protected]
 Elite Legendary Member
 Posts: 10392
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:508 members
 GMAT Score:800
Hi LulaBrazilia,
Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a faster way of looking at it though...
Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship...so Q/P > 1. The question ask which of the 5 options is greater than 1....
That's answer E
GMAT assassins aren't born, they're made,
Rich
Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a faster way of looking at it though...
Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship...so Q/P > 1. The question ask which of the 5 options is greater than 1....
That's answer E
GMAT assassins aren't born, they're made,
Rich

 Junior  Next Rank: 30 Posts
 Posts: 25
 Joined: 04 Mar 2015
 Location: India
 Thanked: 1 times
In answer choice D, if p=1, q=2, then q/(pÂ²)= 2/1Â²= 2/1=2 >1
[email protected] wrote:Given: p/q < 1LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?
A) âˆš(p/q)
B) p/(pÂ²)
C) p/2q
D) q/(pÂ²)
E) q/p
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q
Which of the following MUST be greater than 1?
IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty testmaker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.
E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.
A) âˆš(p/q)
Let p = 1 and q = 4 to get: âˆš(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A
B) p/(pÂ²)
Let p = 2 to get: 2/(2Â²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B
C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C
D) q/(pÂ²)
Let p = 1 and q = 2 to get: 1/(2Â²) = 1/4
1/4 is NOT greater than 1, so ELIMINATE D
STOP.
Since we have eliminated A, B, C and D, the correct answer must be E
Cheers,
Brent
GMAT/MBA Expert
 [email protected]
 Elite Legendary Member
 Posts: 10392
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:508 members
 GMAT Score:800
Hi Priyaranjan,
You are correct; Brent's example doesn't actually eliminate Answer D. You could use P=2 and Q=3 though  and THAT example would eliminate Answer D.
GMAT assassins aren't born, they're made,
Rich
You are correct; Brent's example doesn't actually eliminate Answer D. You could use P=2 and Q=3 though  and THAT example would eliminate Answer D.
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15795
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1267 members
 GMAT Score:770
Nice catch, Priyaranjan!Priyaranjan wrote:In answer choice D, if p=1, q=2, then q/(pÂ²)= 2/1Â²= 2/1=2 >1
[email protected] wrote:Given: p/q < 1LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?
A) âˆš(p/q)
B) p/(pÂ²)
C) p/2q
D) q/(pÂ²)
E) q/p
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q
Which of the following MUST be greater than 1?
IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty testmaker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.
E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.
A) âˆš(p/q)
Let p = 1 and q = 4 to get: âˆš(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A
B) p/(pÂ²)
Let p = 2 to get: 2/(2Â²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B
C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C
D) q/(pÂ²)
Let p = 1 and q = 2 to get: 1/(2Â²) = 1/4
1/4 is NOT greater than 1, so ELIMINATE D
STOP.
Since we have eliminated A, B, C and D, the correct answer must be E
Cheers,
Brent
I have edited my response.
Cheers,
Brent