What is the value of xyz?

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.

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

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

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

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.

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!!

[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.

Below explanation resolved my doubts. Thanks!!

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

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. ?

Posted from my mobile device

Any clarification on my doubt chetan.

Posted from my mobile device

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

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.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.