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# What is the value of x/yz?

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What is the value of x/yz? [#permalink]

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08 Mar 2009, 19:28
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What is the value of x/yz?

(1) x = y/2 and z = 2x/5
(2) x/z = 5/2 and 1/y = 1/10

[Reveal] Spoiler:
Hi guys, this was written before I saw the post on how to write mathematically correct in the forum.

DS #90:

My question about this problem has to do with part 1. The question is fairly simple: Why in part 1 can’t I make all signs match up and equal x? x/yz would then look like this in the way I did it: x / 2x*2x/5.

Here is what the book says:

(1) From this, z can be expressed in terms of y by substituting y/2 for x in the equation z=2x/5, which gives us z=2(2/5) / 5= y/5. The value of x/yz in terms of y is then y/2 / y(y/5) = y/2(5/y[squared])=5/2y. This expression cannot be evaluated further since no information is given about the value of y; not sufficient. (BCE).

Here is how I did it:

What I did is take x=y/2 and make it 2x=y (which Quant book did not do), which then gave me: x / 2x*2x/5, which gave me x / 4x/5, which equals 5x / 4x, and I get 5/4. Meaning I mark this as AD and move to part 2.

Part 2 is easier to solve because we just plug in: y=10, x=5, z=2. 5/10*2=1/4, for which I pick letter D as my answer because both solutions by them selves are sufficient.

One of the big problems I see with my answer is that in part 1 I got 5/4, and in part 2 I got ¼, which is a contradiction and according to MGMAT, I did something wrong.

Please explain this problem and let me know whether and if so, then why I am wrong.

Thanks,

FinanceGuy25
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Jul 2013, 04:12, edited 1 time in total.
Edited the question and added the OA
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08 Mar 2009, 20:09
financeguy25 wrote:
Hi guys, this was written before I saw the post on how to write mathematically correct in the forum.

DS #90:

What is the value of x / yz ?

1. x=y/2 and z=2x/5
2. x/z=5/2 and 1/y=1/10

My question about this problem has to do with part 1. The question is fairly simple: Why in part 1 can’t I make all signs match up and equal x? x/yz would then look like this in the way I did it: x / 2x*2x/5.

Here is what the book says:

(1) From this, z can be expressed in terms of y by substituting y/2 for x in the equation z=2x/5, which gives us z=2(2/5) / 5= y/5. The value of x/yz in terms of y is then y/2 / y(y/5) = y/2(5/y[squared])=5/2y. This expression cannot be evaluated further since no information is given about the value of y; not sufficient. (BCE).

Here is how I did it:

What I did is take x=y/2 and make it 2x=y (which Quant book did not do), which then gave me: x / 2x*2x/5, which gave me x / 4x/5, which equals 5x / 4x, and I get 5/4. Meaning I mark this as AD and move to part 2.

Part 2 is easier to solve because we just plug in: y=10, x=5, z=2. 5/10*2=1/4, for which I pick letter D as my answer because both solutions by them selves are sufficient.

One of the big problems I see with my answer is that in part 1 I got 5/4, and in part 2 I got ¼, which is a contradiction and according to MGMAT, I did something wrong.

Please explain this problem and let me know whether and if so, then why I am wrong.

Thanks,

FinanceGuy25

Note the red part:

x/yz = x/[(2x*2x)/5] = 5x/4x^2 = 5/4x
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08 Mar 2009, 20:28
we can write z = 2y/10

x = y/2

then (y/2) / ((y*y)/5) = 5/2y

so A is insufficient
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08 Mar 2009, 21:01
Hey guys,

Thanks for the help...Thanks GMAT Tiger for pointing out the mistake, I forgot that 2x*2x=4x[Squared], not just 4x.

Thanks,

Financeguy25
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Re: What is the value of x / yz ? [#permalink]

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05 Jul 2013, 03:48
financeguy25 wrote:
What is the value of x / yz ?

1. x=y/2 and z=2x/5
2. x/z=5/2 and 1/y=1/10

My question about this problem has to do with part 1. The question is fairly simple: Why in part 1 can’t I make all signs match up and equal x? x/yz would then look like this in the way I did it: x / 2x*2x/5.

Here is what the book says:

(1) From this, z can be expressed in terms of y by substituting y/2 for x in the equation z=2x/5, which gives us z=2(2/5) / 5= y/5. The value of x/yz in terms of y is then y/2 / y(y/5) = y/2(5/y[squared])=5/2y. This expression cannot be evaluated further since no information is given about the value of y; not sufficient. (BCE).

Hi Bunuel/Instructors,
I have a doubt :
(In red above) how can we cancel Y in numerator with Y in denominator, if the problem doesnt states: y IS NOT= 0.
As the cancellation of Y(or for any variable) involves/multiplication or division by Y on both ends.

So far as I understand GMAT has marked statements in many DS Qs as insuffiecient on this ground stating "we cant divide by a variable unless it is mentioned as non zero"

I observed similar things in Q57(where m/n = 5/3 has been cross multiplied to 5n =3m) - they ignored the point that if m or n is 0 then the answer B wont be SUFFICIENT.

& Q15(in option B, they have ignored the case of x=0, which if true makes B not sufficient as it also the solution also involves division by a variable )

ARE there any particular scenarios in which we are allowed to divide/multiply varibles or transfer them by cross multiplication in an equation.
OR where am i lacking in my basics ?

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Re: What is the value of x / yz ? [#permalink]

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05 Jul 2013, 04:40
Expert's post
3
This post was
BOOKMARKED
p111 wrote:
financeguy25 wrote:
What is the value of x / yz ?

1. x=y/2 and z=2x/5
2. x/z=5/2 and 1/y=1/10

My question about this problem has to do with part 1. The question is fairly simple: Why in part 1 can’t I make all signs match up and equal x? x/yz would then look like this in the way I did it: x / 2x*2x/5.

Here is what the book says:

(1) From this, z can be expressed in terms of y by substituting y/2 for x in the equation z=2x/5, which gives us z=2(2/5) / 5= y/5. The value of x/yz in terms of y is then y/2 / y(y/5) = y/2(5/y[squared])=5/2y. This expression cannot be evaluated further since no information is given about the value of y; not sufficient. (BCE).

Hi Bunuel/Instructors,
I have a doubt :
(In red above) how can we cancel Y in numerator with Y in denominator, if the problem doesnt states: y IS NOT= 0.
As the cancellation of Y(or for any variable) involves/multiplication or division by Y on both ends.

So far as I understand GMAT has marked statements in many DS Qs as insuffiecient on this ground stating "we cant divide by a variable unless it is mentioned as non zero"

I observed similar things in Q57(where m/n = 5/3 has been cross multiplied to 5n =3m) - they ignored the point that if m or n is 0 then the answer B wont be SUFFICIENT.

& Q15(in option B, they have ignored the case of x=0, which if true makes B not sufficient as it also the solution also involves division by a variable )

ARE there any particular scenarios in which we are allowed to divide/multiply varibles or transfer them by cross multiplication in an equation.
OR where am i lacking in my basics ?

What is the value of x/yz?

(1) $$x = \frac{y}{2}$$ and $$z = \frac{2x}{5}$$. If $$y=10$$, then $$x=5$$, $$z=2$$ and in this case $$\frac{x}{yz}=\frac{5}{20}=\frac{1}{4}$$ BUT if $$y=20$$, then $$x=10$$, $$z=4$$ and in this case $$\frac{x}{yz}=\frac{10}{80}=\frac{1}{8}$$. Not sufficient.

(2) $$\frac{x}{z} = \frac{5}{2}$$ and $$\frac{1}{y} = \frac{1}{10}$$. Multiply these two equations: $$\frac{x}{yz}=\frac{5}{20}$$. Sufficient.

1. Yes, it would be better if the stem stated that $$yz\neq{0}$$. If you don't state that, then x=y=z=0 satisfies the first statement and in this case x/(yz) is undefined.

2. As for m/n = 5/3. This equation already implies that neither of them is zero: if m=0, then m/n = 0 and not 5/3 and if n=0, then m/n is not defined, and not 5/3. So, in this case we can write 3m = 5n.

3. I don't know what question is Q15.

Hope it helps.
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Re: What is the value of x / yz ? [#permalink]

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05 Jul 2013, 06:24
Hi,
Appologies for the PM, I wasnt aware.

Bunuel wrote:
1. Yes, it would be better if the stem stated that $$yz\neq{0}$$. If you don't state that, then x=y=z=0 satisfies the first statement and in this case x/(yz) is undefined.

I think you understand my doubt. The scenarios(x,y,z=0) will make the solution undefined. Hence answer E. (Thats the way i solved, considering all scenarios)
SO why are we not picking these values as well? The statement is meant to be true for all real numbers ~ RIGHT ?
How to decide between option D(here) & option E for such questions in exam.

Bunuel wrote:
3. I don't know what question is Q15.

It is question 15 from Data sufficiency & Q57 is question 57.
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Re: What is the value of x / yz ? [#permalink]

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05 Jul 2013, 06:36
p111 wrote:
Hi,
Appologies for the PM, I wasnt aware.

Bunuel wrote:
1. Yes, it would be better if the stem stated that $$yz\neq{0}$$. If you don't state that, then x=y=z=0 satisfies the first statement and in this case x/(yz) is undefined.

I think you understand my doubt. The scenarios(x,y,z=0) will make the solution undefined. Hence answer E. (Thats the way i solved, considering all scenarios)
SO why are we not picking these values as well? The statement is meant to be true for all real numbers ~ RIGHT ?
How to decide between option D(here) & option E for such questions in exam.

Bunuel wrote:
3. I don't know what question is Q15.

It is question 15 from Data sufficiency & Q57 is question 57.

The answer to the question is neither D nor E, it's B.

(1) is not sufficient irrespective whether you have $$yz\neq{0}$$ condition or not. The point is that, their solution for (1) is not 100% correct since it's not mentioned that $$yz\neq{0}$$.

(2) is still sufficient as shown in my post above.

As for Q15 and Q57: I don't know what questions are you talking about. Please post them.
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Re: What is the value of x/yz? [#permalink]

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04 May 2015, 18:54
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Re: What is the value of x/yz? [#permalink]

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21 May 2016, 09:58
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Re: What is the value of x/yz? [#permalink]

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16 Sep 2016, 15:54
x/yz = ?

(1) x = y/2 and z = 2x/5

rewrite first eq as y = 2x and plug into original equation

x/[(2x)(2x/5)] = 5/4x --> we still don't know the exact value of the original equation

(2) x/z = 5/2 and 1/y = 1/10

(5/2)(1/10) = 5/20 --> we have a value!!!

Therefore, (2) is sufficient & B is the correct answer
Re: What is the value of x/yz?   [#permalink] 16 Sep 2016, 15:54
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