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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]

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08 Apr 2013, 04:25
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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, 05:50, 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]

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08 Apr 2013, 05:57
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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]

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08 Apr 2013, 06:12
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, 06:22, 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]

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08 Apr 2013, 06:14
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]

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08 Apr 2013, 06:20
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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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Intern
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Kudos [?]: 3 [0], given: 2

Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink]

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08 Apr 2013, 18:23
ok, 11/10z would fit the answer. Thanks guys.
But B and E aren't really typos, E is actually 2+z/5.
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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]

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29 Oct 2015, 16:20
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: $$\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}$$

Edited: Thanks Bunuel !

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3$$\frac{z}{4}$$ but then later you re-write this as $$\frac{3}{4}$$z

Isn't y a mixed number that should be $$\frac{12+z}{4}$$?
Math Expert
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Posts: 35326
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Kudos [?]: 85872 [0], given: 10256

Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value [#permalink]

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30 Oct 2015, 01:34
nicksson 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: $$\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}$$

Edited: Thanks Bunuel !

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3$$\frac{z}{4}$$ but then later you re-write this as $$\frac{3}{4}$$z

Isn't y a mixed number that should be $$\frac{12+z}{4}$$?

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.
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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]

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30 Oct 2015, 03:34
Bunuel wrote:
nicksson 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: $$\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}$$

Edited: Thanks Bunuel !

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3$$\frac{z}{4}$$ but then later you re-write this as $$\frac{3}{4}$$z

Isn't y a mixed number that should be $$\frac{12+z}{4}$$?

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.

How do you know when it's a mixt number and when it is 3/4*z because to me they look the same?
Math Expert
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Posts: 35326
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Kudos [?]: 85872 [1] , given: 10256

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

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30 Oct 2015, 05:17
1
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Expert's post
nicksson wrote:
Bunuel wrote:
nicksson wrote:

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3$$\frac{z}{4}$$ but then later you re-write this as $$\frac{3}{4}$$z

Isn't y a mixed number that should be $$\frac{12+z}{4}$$?

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.

How do you know when it's a mixt number and when it is 3/4*z because to me they look the same?

If there is a variable involved it's always a multiplication (other case will be explicitly stated).
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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]

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16 Dec 2015, 19:13
please have the question removed or edited.
Re: If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value   [#permalink] 16 Dec 2015, 19:13
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