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What is the value of xyz? [#permalink]
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26 Dec 2013, 10:45
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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?
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Re: What is the Value of xyz? [#permalink]
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26 Dec 2013, 10:57
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
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Re: What is the Value of xyz? [#permalink]
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26 Dec 2013, 11:11
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.



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Re: What is the Value of xyz? [#permalink]
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26 Dec 2013, 15:14
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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 suk1234I'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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Re: What is the Value of xyz? [#permalink]
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27 Dec 2013, 01:48
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 suk1234I'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.



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Re: What is the value of xyz? [#permalink]
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08 Mar 2016, 04:41
xyz=?
St.1 xyzxy=0 => xy(z1)=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? [#permalink]
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Updated on: 08 May 2016, 21:30
what is the value of xyz? (1) xyzxy=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.



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what is the value of xyz? [#permalink]
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08 May 2016, 21:16
chetan86 wrote: what is the value of xyz? (1) xyzxy=0 (2) Either x=0 or y=0 Hi, you will have to relook into OA or the typo erros .. (1) \(xyzxy=0\).. \(xy(z1) = 0...\) either z=1 or xy = 0... if z=1 and xy is NOT equal to 0.. xyz can be any nonzero integer depending on xy.. If xy =0, ans will be 0.. Insuff (2) Either x=0 or y=0In any case , xyz will be 0.. Suff B.. NOTE  Pl Check before posting and post correctly. Merging topics
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Re: what is the value of xyz? [#permalink]
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08 May 2016, 21:23
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) xyzxy=0 (2) Either x=0 or y=0 Hi, you will have to relook into OA or the typo erros .. (1) \(xyzxy=0\).. \(xy(z1) = 0...\) either z=1 or xy = 0... if z=1 and xy is NOT equal to 0.. xyz can be any nonzero integer depending on xy.. If xy =0, ans will be 0.. Insuff (2) Either x=0 or y=0In any case , xyz will be 0.. Suff B..



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Re: what is the value of xyz? [#permalink]
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08 May 2016, 21:27
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) xyzxy=0 (2) Either x=0 or y=0 Hi, you will have to relook into OA or the typo erros .. (1) \(xyzxy=0\).. \(xy(z1) = 0...\) either z=1 or xy = 0... if z=1 and xy is NOT equal to 0.. xyz can be any nonzero integer depending on xy.. If xy =0, ans will be 0.. Insuff (2) Either x=0 or y=0In 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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08 May 2016, 21:30
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!!



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Re: what is the value of xyz? [#permalink]
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08 May 2016, 22:05
[quote="chetan86"]what is the value of xyz? (1) xyzxy=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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Re: what is the value of xyz? [#permalink]
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09 May 2016, 04:52
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 suk1234I'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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