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# The quotient of x and y is 2. If x is 75% of z, which is

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The quotient of x and y is 2. If x is 75% of z, which is [#permalink]  18 Mar 2018, 06:13
Expert's post
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Question Stats:

28% (00:00) correct 71% (02:12) wrong based on 7 sessions
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. $$\frac{21}{8}y$$

Drill 2
Question: 7
Page: 498
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

Re: The quotient of x and y is 2. If x is 75% of z, which is [#permalink]  18 Mar 2018, 07:28
Expert's post
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).
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Sandy
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Re: The quotient of x and y is 2. If x is 75% of z, which is [#permalink]  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. $$\frac{21}{8}y$$

Drill 2
Question: 7
Page: 498

$$\frac{3}{4}y$$larger ?

the stem is confusing!
Re: The quotient of x and y is 2. If x is 75% of z, which is   [#permalink] 19 Mar 2018, 19:06
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