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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
x/w- x/y=0 and w^2 + 4 = 4w
[#permalink]
23 Jul 2022, 06:49
23 Jul 2022, 06:49
1
1
Bookmarks
00:00
Question Stats:
30% (01:05) correct
69% (01:43) wrong based on 13 sessions
Hide Show timer Statistics
\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
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.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
\(2\) |
\(y\) |
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.
x/w- x/y=0 and w^2 + 4 = 4w
[#permalink]
23 Jul 2022, 14:41
23 Jul 2022, 14:41
1
1
Bookmarks
GreenlightTestPrep wrote:
\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
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.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
\(2\) |
\(y\) |
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.
In my opinion, it is option D. It is not necessary to do a painstaking mathematical job to answer this question, for the following reason:
\(x/w - x/y = 0\)
It is not stated that x must be different from zero. The last implies that, if x = 0, any value of w and y fulfills the above equality. In other words, y could be 100000000, or -100000000000, regardless of the value of w, and the equality would be fulfilled.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x/w- x/y=0 and w^2 + 4 = 4w
[#permalink]
24 Jul 2022, 06:46
24 Jul 2022, 06:46
2
GreenlightTestPrep wrote:
\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
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.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
\(2\) |
\(y\) |
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.
I created this question to highlight an important consideration when comparing two equivalent fractions.
If we know that \(\frac{x}{w}=\frac{x}{y}\), we can't then conclude that \(w = y\) (even though both fractions have the same numerator), since it COULD be the case that \(x = 0\), in which case we have \(\frac{0}{w}=\frac{0}{y}\).
Notice that the equation \(\frac{0}{w}=\frac{0}{y}\) holds true for all nonzero values of \(w\) and \(y\).
So, we can't necessarily conclude that \(w = y\)
So, from the given equations, it could be the case that \(x = 0\), \(w = 2\) and \(y = 1\), in which case Quantity A is greater.
Or it could be the case that \(x = 0\), \(w = 2\) and \(y = 3\), in which case Quantity B is greater.
Answer: D
