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555-605 Level|   Algebra|      
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suk1234
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What is the value of xyz? 26 Dec 2013, 10:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

66% (01:13) correct 34% (01:10) wrong based on 511 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


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The see the OA, I think it's incorrect. What's your opinion?
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E
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What is the value of xyz? 26 Dec 2013, 10:57
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suk1234
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?
Show more
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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What is the value of xyz? 26 Dec 2013, 11:11
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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?
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 :-)
Show more

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.
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What is the value of xyz? 26 Dec 2013, 15:14
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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.
Show more
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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What is the value of xyz? 27 Dec 2013, 01:48
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suk1234
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 :-)
Show more
Oh I see, where I was going wrong with it.Thank Mike that was an amazing explanation.
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What is the value of xyz? 08 Mar 2016, 04:41
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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
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What is the value of xyz? Updated on: 08 May 2016, 21:30
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.
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what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0 or z=1
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What is the value of xyz? 08 May 2016, 21:16
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what is the value of xyz?
(1) xyz-xy=0
(2) Either x=0 or y=0
Show more


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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What is the value of xyz? 08 May 2016, 21:23
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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
chetan86
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..
Show more
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What is the value of xyz? 08 May 2016, 21:27
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chetan86
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
chetan86
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..
Show more

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? 08 May 2016, 21:30
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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
Show more

I have updated the question. Thanks!!
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What is the value of xyz? 08 May 2016, 22:05
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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.
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What is the value of xyz? 09 May 2016, 04:52
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Below explanation resolved my doubts. Thanks!!

mikemcgarry
suk1234
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 :-)
Show more
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What is the value of xyz? 08 Sep 2020, 18:31
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chetan86
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
Show more


chetan nick
1) Can you elaborate on difference between Either x=0 or y=0 and xy = 0. You said in an answer that both statements are not same.

2) Also, in xy (z-1) = 0. Either xy=0 or Z=1
A)Taking z=1,putting value of z in the equation we get xy=0
so, xyz will be = (0) x 1 = 0
Whatever will be the value of xy, the product will be zero.

B) Similarly, Taking xy=0, xyz=0 whatever be the value of z

Could you please tell what is wrong with the above concept ?
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What is the value of xyz? 08 Sep 2020, 19:11
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chetan2u
chetan86
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


chetan nick
1) Can you elaborate on difference between Either x=0 or y=0 and xy = 0. You said in an answer that both statements are not same.

2) Also, in xy (z-1) = 0. Either xy=0 or Z=1
A)Taking z=1,putting value of z in the equation we get xy=0
so, xyz will be = (0) x 1 = 0
Whatever will be the value of xy, the product will be zero.

B) Similarly, Taking xy=0, xyz=0 whatever be the value of z

Could you please tell what is wrong with the above concept ?
Show more


Hi

1) When xy=0, we cannot be sure what is 0, but at least one of the x and y is surely 0. That is why either x=0 or y=0 or both x and y are 0.
2) xy(z-1)=0...
When z=1, xy(1-1)=xy*0=0, so xy can be 0,10,100 as (anything)*0=0
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What is the value of xyz? 08 Sep 2020, 21:13
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chetan2u
chetan86
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


chetan nick
1) Can you elaborate on difference between Either x=0 or y=0 and xy = 0. You said in an answer that both statements are not same.

2) Also, in xy (z-1) = 0. Either xy=0 or Z=1
A)Taking z=1,putting value of z in the equation we get xy=0
so, xyz will be = (0) x 1 = 0
Whatever will be the value of xy, the product will be zero.

B) Similarly, Taking xy=0, xyz=0 whatever be the value of z

Could you please tell what is wrong with the above concept ?


Hi

1) When xy=0, we cannot be sure what is 0, but at least one of the x and y is surely 0. That is why either x=0 or y=0 or both x and y are 0.
2) xy(z-1)=0...
When z=1, xy(1-1)=xy*0=0, so xy can be 0,10,100 as (anything)*0=0
Show more

Thanks for your reply Chetan.
But my question is why should we be concerned about specific values of X and Y. Whatever be the value of X & Y, we need to find the product of x, y & z i.e. xyz = ?

We have value of XY and Z and hence we can find the value of xyz. ?

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Any clarification on my doubt chetan.

Posted from my mobile device
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What is the value of xyz? 10 Sep 2020, 03:04
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Any clarification on my doubt chetan.

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Hi

I am sorry but I have not understood how you have got the values of xy and z.
Statement II tells you either xy=0 or z=1
xy=0.....xyz will be 0 irrespective of value of z
z=1....xyz will depend on xy and we cannot say what is xy. If xy =0, xyz =0, but if xy=7, xyz=7
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Gauravji21
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What is the value of xyz? 10 Sep 2020, 17:13
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chetan2u
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Any clarification on my doubt chetan.

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Hi

I am sorry but I have not understood how you have got the values of xy and z.
Statement II tells you either xy=0 or z=1
xy=0.....xyz will be 0 irrespective of value of z
z=1....xyz will depend on xy and we cannot say what is xy. If xy =0, xyz =0, but if xy=7, xyz=7
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Hi Chetan
Thanks for your reply. I was doing it in a wrong way. I was actually putting value of Z=1 in the equation xy(z−1)=0 whereas I was supposed to put the value so obtained from St1 equation in equation in question stem i.e. xyz = 0.
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What is the value of xyz? 24 Jun 2024, 06:21
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From S1, we get xyz =xy (Insufficient)
From S2 we can find xyz =0 only if x=0 or y=0 but if z=0 then xyz =xy (Insufficient)
see from both statements together also we are unable to get any value of xyz, coz both ends in same result xyz=xy
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