GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
0 < xy
[#permalink]
07 Jun 2017, 01:18
07 Jun 2017, 01:18
1
Expert Reply
9
Bookmarks
00:00
Question Stats:
72% (01:49) correct
27% (01:46) wrong based on 259 sessions
Hide Show timer Statistics
\(0 < xy\)
Quantity A |
Quantity B |
\(\frac{5}{2x} - \frac{2}{2y}\) |
\(\frac{5y-2x}{2x-2y}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 0 < xy
[#permalink]
09 Jun 2017, 10:37
09 Jun 2017, 10:37
4
1
Bookmarks
Carcass wrote:
\(0 < xy\)
Quantity A |
Quantity B |
\(\frac{5}{2x} - \frac{2}{2y}\) |
\(\frac{5y-2x}{2x-2y}\) |
Given:
Quantity A: 5/2x - 2/2y
Quantity B: (5y-2x)/(2x-2y)
Let's see what happens if we rewrite Quantity A as one big fraction.
First get common denominators...
Quantity A: 5y/2xy - 2x/2yx
Quantity B: (5y-2x)/(2x-2y)
Combine to get:
Quantity A: (5y-2x)/2yx
Quantity B: (5y-2x)/(2x-2y)
NICE!! This numerators are the same for both fractions.
This gives me the opportunity to use a strategy I call "Looking for Equality" (see our video below for more on this)
I can see that if I choose an x- and y-value that makes the numerators both zero, this will speed up my solution. You'll see why shortly.
I can see that, if x = 5 and y = 2, then we can plug these values into the quantities to get:
Quantity A: [5(2)-2(5)]/(2)(2)(5)
Quantity B: [5(2)-2(5)]/[2(5)-2(2)]
Evaluate:
Quantity A: 0
Quantity B: 0
So, when x = 5 and y = 2 the quantities are EQUAL.
The correct answer is EITHER C or D
At this point, every pair of x- and y-values will either yield equal quantities or not.
Let's plug in super-easy numbers.
We'll plug in x = 1 and y = 1
We get:
Quantity A: [5(1)-2(1)]/(2)(1)(1)
Quantity B: [5(1)-2(1)]/[2(1)-2(1)]
Evaluate:
Quantity A: 3/2
Quantity B: 3/0
These quantities are definitely NOT EQUAL.
Answer:
Show: ::
D
RELATED VIDEOS
General Discussion
Re: 0 < xy
[#permalink]
30 Jan 2018, 10:47
30 Jan 2018, 10:47
2
From the given condition, x and y have to both positive or negative.
Now putting value x=1, y=1
Q.A 3/2 Q.B undefined
Now putting x=1,y=2
Q.A 2 Q.B -4 , Q.A>Q.B
Now putting x=-1,y=-1
Q.A -3/2 Q.B undefined
So the relation can't be determined.
Now putting value x=1, y=1
Q.A 3/2 Q.B undefined
Now putting x=1,y=2
Q.A 2 Q.B -4 , Q.A>Q.B
Now putting x=-1,y=-1
Q.A -3/2 Q.B undefined
So the relation can't be determined.
