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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value

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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 03:25
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If w=\frac{1+x\frac{y}{z^2}}{x+y}, x=\frac{z}{2}, and y=3\frac{z}{4},what is the value of w in terms of z?

A. 11z/10
B. 2z/5
C. 3z/10
D. 11z/10
E. 2z/5

I tried to solve the problem several times, but still didn't get the OA.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 08 Apr 2013, 04:50, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 04:57
Expert's post
sandra1122 wrote:
If w=\frac{1+x\frac{y}{z^2}}{x+y}, x=\frac{z}{2}, and y=3\frac{z}{4},what is the value of w in terms of z?

A. 11z/10
B. 2z/5
C. 3z/10
D. 11z/10
E. 2z/5

I tried to solve the problem several times, but still didn't get the OA.


Notice that options A and D are the same, as well as options B and E, so there are typos in answer choices.

In order A to be the correct answer it should read 11/(10z).

Say z=4, then x=\frac{z}{2}=2, and y=3\frac{z}{4}=3.

So, in this case we'd have that x=2, y=3 and z=4. Plug these values in the fraction to get w=11/40. Now, plug z=4 into the answer choices to see which one yields 11/40. Only A fits (assuming that there IS a typo and A actually must be 11/(10z)).

Hope it helps.
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Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 05:12
Numerator : w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =
1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}
Denominator: \frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z
All together: \frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}

Edited: Thanks Bunuel !
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Last edited by Zarrolou on 08 Apr 2013, 05:22, edited 1 time in total.
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Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 05:14
Expert's post
Zarrolou wrote:
Numerator : w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =
1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}
Denominator: \frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z
All together: \frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5}z=\frac{11}{10}z


(11/8)/(5z/4)=11/(10z) not 11z/10.
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Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 05:20
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Bunuel wrote:
Zarrolou wrote:
Numerator : w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =
1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}
Denominator: \frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z
All together: \frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5}z=\frac{11}{10}z


(11/8)/(5z/4)=11/(10z) not 11z/10.


You're right. Typing mistake, I went MAD with all those [fraction][/fraction] Tags!
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Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink] New post 08 Apr 2013, 17:23
ok, 11/10z would fit the answer. Thanks guys.
But B and E aren't really typos, E is actually 2+z/5.
Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value   [#permalink] 08 Apr 2013, 17:23
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