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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
_________________

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.

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.

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.

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
_________________

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

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
_________________

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

[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.

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.

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