Author 
Message 
TAGS:

Hide Tags

Manager
Status: GMAT BATTLE  WIN OR DIE
Joined: 02 May 2011
Posts: 166
Concentration: General Management, Entrepreneurship
GMAT Date: 12222011
GPA: 3.81
WE: General Management (Hospitality and Tourism)

If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
18 Jun 2011, 04:40
2
This post received KUDOS
33
This post was BOOKMARKED
Question Stats:
67% (01:28) correct
33% (00:39) wrong based on 829 sessions
HideShow timer Statistics
If xy + z = x(y + z), which of the following must be true? A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0
Official Answer and Stats are available only to registered users. Register/ Login.



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
18 Jun 2011, 05:57
19
This post received KUDOS
9
This post was BOOKMARKED
WishMasterUA wrote: if xy+z=x(y+z) which of the following must be true? 1)X=0 AND Z=0 2)X=1 AND Y=0 3)Y=1 AND Z=0 4)X=1 OR Y=0 5)X=1 OR Z=0 xy+z=xy+xz z=xz xzz=0 z(x1)=0 Means; either z=0 OR x1=0 i.e. x=1 Ans: "E"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 07 Nov 2009
Posts: 305

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
05 Feb 2012, 21:28
WishMasterUA wrote: if xy+z=x(y+z) which of the following must be true? 1)X=0 AND Z=0 2)X=1 AND Y=0 3)Y=1 AND Z=0 4)X=1 OR Y=0 5)X=1 OR Z=0 I agree with the answer i.e. X=1 OR Z=0 But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation???



Math Expert
Joined: 02 Sep 2009
Posts: 39701

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
06 Feb 2012, 01:32
14
This post received KUDOS
Expert's post
16
This post was BOOKMARKED
rohitgoel15 wrote: WishMasterUA wrote: if xy+z=x(y+z) which of the following must be true? 1)X=0 AND Z=0 2)X=1 AND Y=0 3)Y=1 AND Z=0 4)X=1 OR Y=0 5)X=1 OR Z=0 I agree with the answer i.e. X=1 OR Z=0 But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation??? If xy+z=x(y+z), which of the following must be true?A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 Notice that we are asked "which of the following MUST be true"? \(xy+z=x(y+z)\) > \(xy+z=xy+xz\) > \(xy\) cancels out > \(xzz=0\) > \(z(x1)=0\) > EITHER \(z=0\) (in this case \(x\) can take ANY value) OR \(x=1\) (in this case \(z\) can take ANY value). Addressing your questions: it's not necessary \(z=0\) and \(x=1\) both to be simultaneously true. "AND" in the answer choices means that BOTH values must be true, but "OR" in the answer choices means that EITHER value must be true. Answer: E. To elaborate more: As the expression with \(y\) cancels out, we can say that given expression \(xy+z=x(y+z)\) does not depend on value of \(y\). Which means that \(y\) can take ANY value. So all answer choices which specify the exact value of \(y\) are wrong. Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Status: #TeamFuqua
Joined: 01 Jun 2010
Posts: 122
Location: United States
Concentration: General Management, Strategy
GMAT 1: 580 Q37 V32 GMAT 2: 570 Q36 V32 GMAT 3: 680 Q44 V40
WE: Consulting (Consulting)

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
13 Aug 2013, 16:31
Bunuel wrote: rohitgoel15 wrote: WishMasterUA wrote: if xy+z=x(y+z) which of the following must be true? 1)X=0 AND Z=0 2)X=1 AND Y=0 3)Y=1 AND Z=0 4)X=1 OR Y=0 5)X=1 OR Z=0 I agree with the answer i.e. X=1 OR Z=0 But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation??? If xy+z=x(y+z), which of the following must be true?A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 Notice that we are asked "which of the following MUST be true"? \(xy+z=x(y+z)\) > \(xy+z=xy+xz\) > \(xy\) cancels out > \(xzz=0\) > \(z(x1)=0\) > EITHER \(z=0\) (in this case \(x\) can take ANY value) OR \(x=1\) (in this case \(z\) can take ANY value). Addressing your questions: it's not necessary \(z=0\) and \(x=1\) both to be simultaneously true. "AND" in the answer choices means that BOTH values must be true, but "OR" in the answer choices means that EITHER value must be true. Answer: E. To elaborate more: As the expression with \(y\) cancels out, we can say that given expression \(xy+z=x(y+z)\) does not depend on value of \(y\). Which means that \(y\) can take ANY value. So all answer choices which specify the exact value of \(y\) are wrong. Hope it helps. Hi Bunuel, I was wondering if substituting the answer options would be a good approach here? I attempted by substituting the values in each answer option and got both B/D to be valid for the equation in the question. Interestingly, if we simplify the equation we see that in both answer choices we have the value of Y, which is immaterial. It would be great if you can let me know what you think of approaching similar questions through their answer choices. Thanks!
_________________
MBAJunkie



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
13 Jun 2014, 19:48
Bunuel wrote: rohitgoel15 wrote: WishMasterUA wrote: if xy+z=x(y+z) which of the following must be true? 1)X=0 AND Z=0 2)X=1 AND Y=0 3)Y=1 AND Z=0 4)X=1 OR Y=0 5)X=1 OR Z=0 I agree with the answer i.e. X=1 OR Z=0 But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation??? If xy+z=x(y+z), which of the following must be true?A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 Notice that we are asked "which of the following MUST be true"? \(xy+z=x(y+z)\) > \(xy+z=xy+xz\) > \(xy\) cancels out > \(xzz=0\) > \(z(x1)=0\) > EITHER \(z=0\) (in this case \(x\) can take ANY value) OR \(x=1\) (in this case \(z\) can take ANY value). Addressing your questions: it's not necessary \(z=0\) and \(x=1\) both to be simultaneously true. "AND" in the answer choices means that BOTH values must be true, but "OR" in the answer choices means that EITHER value must be true. Answer: E. To elaborate more: As the expression with \(y\) cancels out, we can say that given expression \(xy+z=x(y+z)\) does not depend on value of \(y\). Which means that \(y\) can take ANY value. So all answer choices which specify the exact value of \(y\) are wrong. Hope it helps. Hi Bunuel, Two questions: I took the approach of plugging in answer choices and multiple answers satisfied the "must be true part". Why is that wrong? When you came down to xz=z, why did you take the next step of factoring out the z and equating the whole thing to zero, meaning, why did you get to the point of z(x1)=0? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 39701

Re: if xy+z=x(y+z) which of the following must be true? [#permalink]
Show Tags
14 Jun 2014, 01:45
russ9 wrote: Bunuel wrote: rohitgoel15 wrote: If xy+z=x(y+z), which of the following must be true? A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0
Notice that we are asked "which of the following MUST be true"?
\(xy+z=x(y+z)\) > \(xy+z=xy+xz\) > \(xy\) cancels out > \(xzz=0\) > \(z(x1)=0\) > EITHER \(z=0\) (in this case \(x\) can take ANY value) OR \(x=1\) (in this case \(z\) can take ANY value).
Addressing your questions: it's not necessary \(z=0\) and \(x=1\) both to be simultaneously true. "AND" in the answer choices means that BOTH values must be true, but "OR" in the answer choices means that EITHER value must be true.
Answer: E.
To elaborate more: As the expression with \(y\) cancels out, we can say that given expression \(xy+z=x(y+z)\) does not depend on value of \(y\). Which means that \(y\) can take ANY value. So all answer choices which specify the exact value of \(y\) are wrong.
Hope it helps. Hi Bunuel, Two questions: I took the approach of plugging in answer choices and multiple answers satisfied the "must be true part". Why is that wrong? When you came down to xz=z, why did you take the next step of factoring out the z and equating the whole thing to zero, meaning, why did you get to the point of z(x1)=0? Thanks 1."MUST BE TRUE" questions: These questions ask which of the following MUST be true, or which of the following is ALWAYS true for ALL valid sets of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular valid set of numbers, it will mean that this statement is not always true and hence not a correct answer. So, for "MUST BE TRUE" questions plugin method is good to discard an option but not 100% sure thing to prove that an option is ALWAYS true. As for "COULD BE TRUE" questions: The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer. So, for "COULD BE TRUE" questions plugin method is fine to prove that an option could be true. But here, if for some set of numbers you'll see that an option is not true, it won't mean that there does not exist some other set which will make this option true. 2.To get what x and z could be from xz = z, we should do the way shown in my solution. Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15982

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
23 Jun 2015, 22:07
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 30 Jul 2015
Posts: 2
Concentration: Accounting, Finance

If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
09 Oct 2015, 21:11
MBAjunkie16 wrote: Hi Bunuel,
I was wondering if substituting the answer options would be a good approach here? I attempted by substituting the values in each answer option and got both B/D to be valid for the equation in the question. Interestingly, if we simplify the equation we see that in both answer choices we have the value of Y, which is immaterial. It would be great if you can let me know what you think of approaching similar questions through their answer choices.
Thanks!
Hi Bunuel, I have the same question with MBAjunkie16. What if I substituing the vales in each anwser and got B to be valid? Thank you so much!
_________________
Live the life you love Love the life you live



Intern
Joined: 21 Mar 2015
Posts: 2

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
18 Jan 2016, 23:48
WishMasterUA wrote: If xy + z = x(y + z), which of the following must be true?
A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 x=1 can be easily found out, but then you can you find out the other condition of y or z. It can have multiple answers



Intern
Joined: 14 Aug 2015
Posts: 17

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
23 Jan 2016, 09:14
xy + z = x(y + z) Subtract xy from both side ==> z=xz Remeber we cannot divide by a variable unless we know it is not = 0. So 0=xzz ==> 0=z(x1) ==> z=0 OR x=1



Intern
Joined: 06 Aug 2015
Posts: 3

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
28 Jun 2016, 14:53
Hi everyone! Why, in this case, the option X = 0 and Z = 0 wouldn't apply? I believe an "or" option is better than "and" (more flexible), but that's not the point here. If both X = 0 AND Z = 0, I get 0*0  0 = 0, which also holds (regardless of Y's value).
Thanks!!!



Math Expert
Joined: 02 Sep 2009
Posts: 39701

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
29 Jun 2016, 00:25
nramirez wrote: Hi everyone! Why, in this case, the option X = 0 and Z = 0 wouldn't apply? I believe an "or" option is better than "and" (more flexible), but that's not the point here. If both X = 0 AND Z = 0, I get 0*0  0 = 0, which also holds (regardless of Y's value).
Thanks!!! It's explained several times above, so please go through the discussion. The question asks which of the following MUST be true not COULD be true. Option A (x=0 and y=0) is not necessarily true, thus not correct. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 06 Aug 2015
Posts: 3

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
29 Jun 2016, 03:53
Bunuel wrote: nramirez wrote: Hi everyone! Why, in this case, the option X = 0 and Z = 0 wouldn't apply? I believe an "or" option is better than "and" (more flexible), but that's not the point here. If both X = 0 AND Z = 0, I get 0*0  0 = 0, which also holds (regardless of Y's value).
Thanks!!! It's explained several times above, so please go through the discussion. The question asks which of the following MUST be true not COULD be true. Option A (x=0 and y=0) is not necessarily true, thus not correct. Hope it's clear. Hi Bunuel, thanks for your answer! The A option I got in GMAT Prep is not X = 0 AND Y = 0, but X = 0 AND Z = 0. That's basically why I assume it's a possible option, and failed to see why it isn't. Can you help me here? Thanks!! Posted from my mobile device



Math Forum Moderator
Joined: 13 Apr 2015
Posts: 1485
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
29 Jun 2016, 04:17
Hi nramirez, As stated by Bunuel, this is a must be true question. The only two possible cases are: 1) X has to be equal to 1 or 2) Z has to be equal to 0. So when you plug the values into the equation, one of the two cases will always be satisfied. You are saying that you got the option as X = 0 or Z = 0. Try plugging few values Say, X = 1, Y = 1 and Z = 1 XY + Z = 1 + 1 = 2 X(Y + Z) = 1(1 + 1) = 2 So X = 0 is not a must be true condition. Hope it helps.



Intern
Joined: 29 Nov 2016
Posts: 11

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
16 Apr 2017, 09:09
After getting z=xz , I cancelled out the z and got x=1. So naturally, B, D and E were valid options. A also gave me the equation z=xz which is exactly the same thing so I went with A. What is wrong in my approach?



SVP
Joined: 12 Sep 2015
Posts: 1559
Location: Canada

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
16 Apr 2017, 13:21
hannahkagalwala wrote: After getting z=xz , I cancelled out the z and got x=1. So naturally, B, D and E were valid options. A also gave me the equation z=xz which is exactly the same thing so I went with A. What is wrong in my approach? Once we know that z = xz, we cannot divide both sides by z, because it COULD be the case that z equals zero, and we should never divide by zero. Here's why: We know that (2)(0) = (1)(0) However, if we try to divide by both sides by 0, we may believe that we get: 2 = 1, which of course is not true. Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Manager
Joined: 23 Dec 2013
Posts: 205

Re: If xy+z=x(y+z), which of the following must be true? [#permalink]
Show Tags
25 Jun 2017, 18:03
WishMasterUA wrote: If xy + z = x(y + z), which of the following must be true?
A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 xy + z = xy + xz z = xz zxz = 0 z(1x) = 0 z = 0 or x = 1 so x1 = 0.




Re: If xy+z=x(y+z), which of the following must be true?
[#permalink]
25 Jun 2017, 18:03







