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Intern  Joined: 29 Sep 2013
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Difficulty:   45% (medium)

Question Stats: 58% (01:17) correct 42% (01:16) wrong based on 128 sessions

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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?
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
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2
1
suk1234 wrote:
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?

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 _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 29 Sep 2013
Posts: 45
Re: What is the Value of xyz?  [#permalink]

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mikemcgarry wrote:
suk1234 wrote:
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?

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.
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: What is the Value of xyz?  [#permalink]

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1
1
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 _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 29 Sep 2013
Posts: 45
Re: What is the Value of xyz?  [#permalink]

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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.
Director  G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: What is the value of xyz?  [#permalink]

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xyz=?

St.1 xyz-xy=0 => xy(z-1)=0, so xy=0 or z=1 or both . If xy=0, xyz=0, if z=1, not clear. INSUFF.

St.2 Either x = 0, or y = 0 or z = 1. Again if z=1, not clear. INSUFF.

St1+St2 tell the same, so INSUFF

E
Manager  Joined: 17 Oct 2012
Posts: 60
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what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0 or z=1

Originally posted by chetan86 on 08 May 2016, 21:08.
Last edited by chetan86 on 08 May 2016, 21:30, edited 1 time in total.
Math Expert V
Joined: 02 Aug 2009
Posts: 7978
what is the value of xyz?  [#permalink]

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chetan86 wrote:
what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0

Hi,
you will have to relook into OA or the typo erros ..

(1) $$xyz-xy=0$$..
$$xy(z-1) = 0...$$
either z=1 or xy = 0...
if z=1 and xy is NOT equal to 0.. xyz can be any non-zero integer depending on xy..
If xy =0, ans will be 0..
Insuff

(2) Either x=0 or y=0
In any case , xyz will be 0..
Suff

B..

NOTE - Pl Check before posting and post correctly.
Merging topics
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Yeah, I rechecked the answer, and it is E. Even I am confused about this question so thought to post this question to clear my understandings.
This question is from Advance GMAT Quant.

OE is :
We can test different numeric scenarios for x, y and z using Scenario Charts. Statement (1) tells us that xyz – xy = 0. First, let's factor the equation:
xyz – xy = 0
xy(z – 1) = 0
For this product to equal zero, either x = 0, or y = 0, or z = 1.

Thus if x = 0 or y = 0, then xyz = 0, but if z = 1, then xyz could take on any value. INSUFFICIENT.

Statement (2) tells us that either x = 0 or y = 0 or z = 1. This is the exact same information from Statement (1), so we can eliminate A, B and C by Spotting Identical Statements. Since Statement (1) also proved to be insufficient, we can eliminate D as well.

The correct answer is E.

chetan2u wrote:
chetan86 wrote:
what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0

Hi,
you will have to relook into OA or the typo erros ..

(1) $$xyz-xy=0$$..
$$xy(z-1) = 0...$$
either z=1 or xy = 0...
if z=1 and xy is NOT equal to 0.. xyz can be any non-zero integer depending on xy..
If xy =0, ans will be 0..
Insuff

(2) Either x=0 or y=0
In any case , xyz will be 0..
Suff

B..
Math Expert V
Joined: 02 Aug 2009
Posts: 7978
Re: what is the value of xyz?  [#permalink]

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chetan86 wrote:
Yeah, I rechecked the answer, and it is E. Even I am confused about this question so thought to post this question to clear my understandings.
This question is from Advance GMAT Quant.

OE is :
We can test different numeric scenarios for x, y and z using Scenario Charts. Statement (1) tells us that xyz – xy = 0. First, let's factor the equation:
xyz – xy = 0
xy(z – 1) = 0
For this product to equal zero, either x = 0, or y = 0, or z = 1.

Thus if x = 0 or y = 0, then xyz = 0, but if z = 1, then xyz could take on any value. INSUFFICIENT.

Statement (2) tells us that either x = 0 or y = 0 or z = 1. This is the exact same information from Statement (1), so we can eliminate A, B and C by Spotting Identical Statements. Since Statement (1) also proved to be insufficient, we can eliminate D as well.

The correct answer is E.

chetan2u wrote:
chetan86 wrote:
what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0

Hi,
you will have to relook into OA or the typo erros ..

(1) $$xyz-xy=0$$..
$$xy(z-1) = 0...$$
either z=1 or xy = 0...
if z=1 and xy is NOT equal to 0.. xyz can be any non-zero integer depending on xy..
If xy =0, ans will be 0..
Insuff

(2) Either x=0 or y=0
In any case , xyz will be 0..
Suff

B..

Then there is a error in what you have given as statement 2 and what is mentioned..
as per your Q.. II is "Either x=0 or y=0", whereas the source is giveing in the OE as "Statement (2) tells us that either x = 0 or y = 0 or z = 1"..

Both the statements do NOT mean the same ..
and if statement is - Statement (2) tells us that either x = 0 or y = 0 or z = 1.. ANS will be E
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what is the value of xyz?  [#permalink]

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chetan2u wrote:

Then there is a error in what you have given as statement 2 and what is mentioned..
as per your Q.. II is "Either x=0 or y=0", whereas the source is giveing in the OE as "Statement (2) tells us that either x = 0 or y = 0 or z = 1"..

Both the statements do NOT mean the same ..
and if statement is - Statement (2) tells us that either x = 0 or y = 0 or z = 1.. ANS will be E

I have updated the question. Thanks!!
Manager  Joined: 13 Apr 2016
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Re: what is the value of xyz?  [#permalink]

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[quote="chetan86"]what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0 or z=1

I think the answer has to be E because none of the statement is giving any fix value for any of the variable and also by combining we are not getting any confirmed answer.
Manager  Joined: 17 Oct 2012
Posts: 60
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
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Below explanation resolved my doubts. Thanks!!

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 Non-Human User Joined: 09 Sep 2013
Posts: 13262
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_________________ Re: what is the value of xyz?   [#permalink] 24 Mar 2018, 22:30
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