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.
The quotient of x and y is 2. If x is 75% of z, which is
[#permalink]
18 Mar 2018, 06:13
18 Mar 2018, 06:13
Expert Reply
2
Bookmarks
00:00
Question Stats:
42% (01:42) correct
57% (02:45) wrong based on 14 sessions
Hide Show timer Statistics
The quotient of x and y is 2. If x is 75% of z, which is \(\frac{3}{4}y\)larger than w, what is w in terms of y ?
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
Drill 2
Question: 7
Page: 498
Question: 7
Page: 498
Re: The quotient of x and y is 2. If x is 75% of z, which is
[#permalink]
18 Mar 2018, 07:28
18 Mar 2018, 07:28
1
Expert Reply
Explanation
Translate what you are told into algebra: \(\frac{x}{y}=2\) and \(x=\frac{75}{100}\times z=\frac{3}{4}\times z\).
Notice that the problem then tells you that z is larger than w, not z is of \(\frac{3}{4}\) w.
That means \(z=w+\frac{3}{4}w=(1+\frac{3}{4})w=\frac{7}{4}w\).
At this point, you can either Plug In or do algebra.
To Plug In, choose 4 for w, so z = 7, and \(x=\frac{3}{4}\times 7=\frac{21}{4}\).
If \(\frac{x}{y}=2\), then x = 2y, so \(\frac{21}{4}=2y\); \(y= \frac{21}{8}\).
Now plug \(\frac{21}{8}\) into the answer choices for y to see which hits your target number, w = 4.
Only choice (C) does. Alternatively, to do algebra, combine the first two equations you translated into algebra: \(2y=\frac{3}{4} z\); \(z=\frac{8}{3}\).
Combining this equation with the one you derived above, it follows that \(\frac{8}{3}y= \frac{7}{4}w\), and \(w= \frac{32}{21}y\); the answer is choice (C).
Translate what you are told into algebra: \(\frac{x}{y}=2\) and \(x=\frac{75}{100}\times z=\frac{3}{4}\times z\).
Notice that the problem then tells you that z is larger than w, not z is of \(\frac{3}{4}\) w.
That means \(z=w+\frac{3}{4}w=(1+\frac{3}{4})w=\frac{7}{4}w\).
At this point, you can either Plug In or do algebra.
To Plug In, choose 4 for w, so z = 7, and \(x=\frac{3}{4}\times 7=\frac{21}{4}\).
If \(\frac{x}{y}=2\), then x = 2y, so \(\frac{21}{4}=2y\); \(y= \frac{21}{8}\).
Now plug \(\frac{21}{8}\) into the answer choices for y to see which hits your target number, w = 4.
Only choice (C) does. Alternatively, to do algebra, combine the first two equations you translated into algebra: \(2y=\frac{3}{4} z\); \(z=\frac{8}{3}\).
Combining this equation with the one you derived above, it follows that \(\frac{8}{3}y= \frac{7}{4}w\), and \(w= \frac{32}{21}y\); the answer is choice (C).
Re: The quotient of x and y is 2. If x is 75% of z, which is
[#permalink]
19 Mar 2018, 19:06
19 Mar 2018, 19:06
sandy wrote:
The quotient of x and y is 2. If x is 75% of z, which is \(\frac{3}{4}y\)larger than w, what is w in terms of y ?
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
Drill 2
Question: 7
Page: 498
Question: 7
Page: 498
\(\frac{3}{4}y\)larger ?
the stem is confusing!
