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What is the value of xyz?

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What is the value of xyz? [#permalink] New post 26 Dec 2013, 09:45
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (02:13) correct 31% (01:18) wrong based on 16 sessions
What is the value of xyz?

(1) xyz - xy = 0
(2) Either x = 0, or y = 0 or z = 1


The see the OA, I think it's incorrect. What's your opinion?
[Reveal] Spoiler: OA
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Re: What is the Value of xyz? [#permalink] New post 26 Dec 2013, 09:57
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suk1234 wrote:
What is the value ofxyz?

1) xyz - xy = 0
2) Either x=0, or y=0 or z=1

The see the OA, I think it's incorrect. What's your opinion?

Dear suk1234,
I'm happy to respond. :-)

I think the OA of (E) is correct. First of all, Statement #1 and Statement #2 are logical equivalent, and one implies the other.
If x = 0 or y = 0, then the other could equal anything, z could equal anything, and the product would be zero.
If z = 1, then x & y could equal anything, and the product could equal any value on the continuous infinity of the number line.
Thus, there's no way to determine a definitive value of the product.

Does this make sense? Please let me know if you have any further questions.
Mike :-)
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Mike McGarry
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Re: What is the Value of xyz? [#permalink] New post 26 Dec 2013, 10:11
mikemcgarry wrote:
suk1234 wrote:
What is the value ofxyz?

1) xyz - xy = 0
2) Either x=0, or y=0 or z=1

The see the OA, I think it's incorrect. What's your opinion?

Dear suk1234,
I'm happy to respond. :-)

I think the OA of (E) is correct. First of all, Statement #1 and Statement #2 are logical equivalent, and one implies the other.
If x = 0 or y = 0, then the other could equal anything, z could equal anything, and the product would be zero.
If z = 1, then x & y could equal anything, and the product could equal any value on the continuous infinity of the number line.
Thus, there's no way to determine a definitive value of the product.

Does this make sense? Please let me know if you have any further questions.
Mike :-)


Thank you Mike for the Quick rescue!

Here is how I evaluated Statement 1:

Z=1 and Either X=0 or Y=0 or Both X and Y = 0

Then evaluate all the possible values!
1. (X=0) 0*Y*1=0
2. (Y=0) X*0*1=0
3. (X and Y = 0) 0*0*1=0

I think in case of statement 2 this reasoning doesn't apply because it presents three cases which may or may not be true ( x=0, or y=0 or z=1 either of these can happen or not).
But in case of statement 1 we are definitely sure about the value of XY.
Expert Post
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Magoosh GMAT Instructor
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Re: What is the Value of xyz? [#permalink] New post 26 Dec 2013, 14:14
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Expert's post
suk1234 wrote:
Thank you Mike for the Quick rescue!

Here is how I evaluated Statement 1:

Z=1 and Either X=0 or Y=0 or Both X and Y = 0

Then evaluate all the possible values!
1. (X=0) 0*Y*1=0
2. (Y=0) X*0*1=0
3. (X and Y = 0) 0*0*1=0

I think in case of statement 2 this reasoning doesn't apply because it presents three cases which may or may not be true ( x=0, or y=0 or z=1 either of these can happen or not).
But in case of statement 1 we are definitely sure about the value of XY.

Dear suk1234
I'm happy to respond. :-)

Statement #1 says
xyz - xy = 0
Add xy to both sides:
xyz = xy
(xy)*z = (xy)

Here, we are presented with a choice.
Case One:
If (xy) does not equal zero, then we can divide by (xy), and get z = 1. That's one case, in which (xy) can have any value on the number line other than zero, and z = 1. Here, the product xyz would be equal to xy, and could be anything other than zero.
Case Two:
If (xy) = 0, then z could be anything on the number line. This is the other case. If (xy) = 0, then either x = 0 or y = 0, which will make the product equal zero. (Here, z could be 1, or it could be anything else on the number line.)

You see, the crucial mathematical word is the word "or" ---- either z = 1 OR (xy) = 0. You are interpreting the two requirements as if they are simultaneous, not a mutually exclusive choice. The two cases are actually mutually exclusive.

Does all this make sense?
Mike :-)
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Mike McGarry
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Re: What is the Value of xyz? [#permalink] New post 27 Dec 2013, 00:48
mikemcgarry wrote:
suk1234 wrote:
Thank you Mike for the Quick rescue!

Here is how I evaluated Statement 1:

Z=1 and Either X=0 or Y=0 or Both X and Y = 0

Then evaluate all the possible values!
1. (X=0) 0*Y*1=0
2. (Y=0) X*0*1=0
3. (X and Y = 0) 0*0*1=0

I think in case of statement 2 this reasoning doesn't apply because it presents three cases which may or may not be true ( x=0, or y=0 or z=1 either of these can happen or not).
But in case of statement 1 we are definitely sure about the value of XY.

Dear suk1234
I'm happy to respond. :-)

Statement #1 says
xyz - xy = 0
Add xy to both sides:
xyz = xy
(xy)*z = (xy)

Here, we are presented with a choice.
Case One:
If (xy) does not equal zero, then we can divide by (xy), and get z = 1. That's one case, in which (xy) can have any value on the number line other than zero, and z = 1. Here, the product xyz would be equal to xy, and could be anything other than zero.
Case Two:
If (xy) = 0, then z could be anything on the number line. This is the other case. If (xy) = 0, then either x = 0 or y = 0, which will make the product equal zero. (Here, z could be 1, or it could be anything else on the number line.)

You see, the crucial mathematical word is the word "or" ---- either z = 1 OR (xy) = 0. You are interpreting the two requirements as if they are simultaneous, not a mutually exclusive choice. The two cases are actually mutually exclusive.

Does all this make sense?
Mike :-)

Oh I see, where I was going wrong with it.Thank Mike that was an amazing explanation.
Re: What is the Value of xyz?   [#permalink] 27 Dec 2013, 00:48
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