GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Apr 2019, 21:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is |x| = y + z?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Jul 2010
Posts: 24
Is |x| = y + z?  [#permalink]

### Show Tags

Updated on: 28 Nov 2013, 10:24
10
00:00

Difficulty:

85% (hard)

Question Stats:

57% (01:53) correct 43% (01:48) wrong based on 407 sessions

### HideShow timer Statistics

Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

Originally posted by pgmat on 05 Jun 2012, 16:38.
Last edited by Bunuel on 28 Nov 2013, 10:24, edited 1 time in total.
Edited the OA.
Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 118
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)

### Show Tags

05 Jun 2012, 18:00
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)
_________________
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt
Intern
Joined: 26 Jul 2010
Posts: 24

### Show Tags

05 Jun 2012, 20:19
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.
Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 118
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)

### Show Tags

05 Jun 2012, 20:33
pgmat wrote:
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.

Yeah I also got this wrong the first time because I thought Statement (1) was already sufficient. However, we need Statement (2).
_________________
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt
Intern
Joined: 30 May 2012
Posts: 19
Concentration: Finance, Strategy
GMAT 1: 730 Q49 V41
GPA: 3.39

### Show Tags

06 Jun 2012, 13:14
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

Did you copy this problem down correctly? -x=y+z =/=> x+y=z.
Intern
Joined: 30 May 2012
Posts: 19
Concentration: Finance, Strategy
GMAT 1: 730 Q49 V41
GPA: 3.39

### Show Tags

06 Jun 2012, 13:17
pgmat wrote:
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.

This is where you're incorrect. -x=y+z alone does not imply that x<0 without the condition that y+z >0.
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: Is |x| = y + z? (1) x + y = z (2) x < 0  [#permalink]

### Show Tags

09 Jun 2012, 14:13
1
2
pgmat wrote:
Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

The answer to this question is E, not C.

Consider below 2 cases:
$$x=-1$$, $$y=1$$ and $$z=0$$ --> $$|x|=1$$ and $$y+z=1$$ --> answer YES;
$$x=-1$$, $$y=2$$ and $$z=1$$ --> $$|x|=1$$ and $$y+z=3$$ --> answer NO.

I think you refer to the following question:

Is $$|x|=y-z$$?

Note that $$y-z$$ must be $$\geq{0}$$, because absolute value (in our case $$|x|$$) can not be negative.

Generally question asks whether $$y-z\geq{0}$$ and whether the difference between them equals to $$|x|$$.

(1) x + y = z --> $$-x=y-z$$
if $$x>0$$ --> $$y-z$$ is negative --> no good for us;
if $$x\leq{0}$$ --> $$y-z$$ is positive --> good.

(2) $$x<0$$
Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

Hope it's clear.
_________________
Intern
Joined: 10 May 2012
Posts: 38
Re: Is |x| = y + z? (1) x + y = z (2) x < 0  [#permalink]

### Show Tags

17 Aug 2012, 23:08
Bunuel wrote:
pgmat wrote:
Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

The answer to this question is E, not C.

Consider below 2 cases:
$$x=-1$$, $$y=1$$ and $$z=0$$ --> $$|x|=1$$ and $$y+z=1$$ --> answer YES;
$$x=-1$$, $$y=2$$ and $$z=1$$ --> $$|x|=1$$ and $$y+z=3$$ --> answer NO.

I think you refer to the following question:

Is $$|x|=y-z$$?

Note that $$y-z$$ must be $$\geq{0}$$, because absolute value (in our case $$|x|$$) can not be negative.

Generally question asks whether $$y-z\geq{0}$$ and whether the difference between them equals to $$|x|$$.

(1) x + y = z --> $$-x=y-z$$
if $$x>0$$ --> $$y-z$$ is negative --> no good for us;
if $$x\leq{0}$$ --> $$y-z$$ is positive --> good.

(2) $$x<0$$
Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

Hope it's clear.

Hi ,

Though it looks reasonable , I am not sure on what is wrong with this logic.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 185
Schools: Johnson '15
Re: Is |x| = y + z? (1) x + y = z (2) x < 0  [#permalink]

### Show Tags

18 Aug 2012, 01:00
pgmat wrote:
Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

given that x = y+z or -x=Y+z

so 1. x+Y = z..... not sufficient
2. it does not tell everything either... so not sufficient..

together.... -x+y = z

-x = -y+z, hence not same as given in the question, hence the answer to the main question is NO and with C option we are answering it.
_________________
Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs
Director
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: Is |x| = y + z? (1) x + y = z (2) x < 0  [#permalink]

### Show Tags

20 Aug 2012, 13:33
2
1
pgmat wrote:
Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

(1) $$x = y-z$$. Then $$|x|=|y-z|$$ which is either $$y-z$$ or $$z-y.$$
In order to have $$y+z=y-z$$, necessarily $$z=0$$ and also $$y\geq0.$$
In order to have $$y+z=z-y$$, necessarily $$y=0$$ and also $$z\geq0.$$
Obviously not sufficient.

(2) Clearly not sufficient.

(1) and (2)
We are in the case $$x=y-z<0$$ so $$|x|=z-y$$. For $$|x|=y+z$$ as seen above we need $$y=0$$ and $$z\geq0.$$ Neither condition is guaranteed.
Not sufficient.

_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern
Joined: 05 Mar 2012
Posts: 44
Schools: Tepper '15 (WL)
Re: Is |x| = y + z? (1) x + y = z (2) x < 0  [#permalink]

### Show Tags

22 Aug 2012, 13:59
Answer is E. Plugged in a bunch of numbers.

1) x=3, y=4, z=7 gives us the answer no, but x= -5, y=3, z=2 gives us yes. Insufficient

2) x<0 insufficient since y and z are unknown

Put them together, x=-5, y=3, z=2 gives us yes, but x=-5, y=-7, z=-12 gives us no. Insufficient.
Intern
Joined: 24 Jan 2013
Posts: 37
Re: Is |x| = y + z?  [#permalink]

### Show Tags

29 Nov 2013, 05:40
Hi Bunuel!
I have a doubt.
|x|= y+z gives us two equations..
X= y+ z or -x= y+z
Statement one says x+y=z .. It is not possible to get the above mentioned statements with this equation.
Statement two says x<0 ..this should be sufficient to answer right?

Similarly. In the question |x|= y-z.
We can x= y-z and -x= y-z
Statement one by substituting we get -x= y-z so this should be suffice to right?
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: Is |x| = y + z?  [#permalink]

### Show Tags

29 Nov 2013, 06:05
Hi Bunuel!
I have a doubt.
|x|= y+z gives us two equations..
X= y+ z or -x= y+z
Statement one says x+y=z .. It is not possible to get the above mentioned statements with this equation.
Statement two says x<0 ..this should be sufficient to answer right?

Similarly. In the question |x|= y-z.
We can x= y-z and -x= y-z
Statement one by substituting we get -x= y-z so this should be suffice to right?

Not sure I understand your logic there...

Number plugging proving that E is the answer: is-x-y-z-133977.html#p1094912
Algebraic approach proving the same: is-x-y-z-133977.html#p1114409

Hope this helps.
_________________
Intern
Joined: 24 Jan 2013
Posts: 37
Re: Is |x| = y + z?  [#permalink]

### Show Tags

29 Nov 2013, 12:30
In the question |x|= y-z.
We get two equations I.e.(removing the modulus . x= y-z and -x= y-z
Statement one says x+z =y
Therefore by substituting we get -x= y-z. so this should be suffice to answer right?
As the question stem also has the same equation.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: Is |x| = y + z?  [#permalink]

### Show Tags

29 Nov 2013, 12:46
In the question |x|= y-z.
We get two equations I.e.(removing the modulus . x= y-z and -x= y-z
Statement one says x+z =y
Therefore by substituting we get -x= y-z. so this should be suffice to answer right?
As the question stem also has the same equation.

Posted from my mobile device

Since the correct answer is E, then this is obviously not right.

If $$x\geq{0}$$, the questions asks: is $$x=y+z$$?
If $$x<{0}$$, the questions asks: is $$-x=y+z$$?

When we combine the statements, since it's given that x<0, the questions becomes: is $$-x=y+z$$. From (1) we have that $$-x=y-z$$, which is not sufficient to get whether $$-x=y+z$$.

Consider the examples given here: http://gmatclub.com/forum/is-x-y-z-133977.html#p1094912
_________________
Intern
Joined: 26 Mar 2017
Posts: 27
GMAT 1: 720 Q50 V38
Is |x| = y + z?  [#permalink]

### Show Tags

25 Apr 2017, 12:38
pgmat wrote:
Is |x| = y + z?

(1) x + y = z
(2) x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

(I think the question could have been better stated.)

statement-1: Insufficient.
rewrite x+y=z as x=z-y.
If (z=0 and y=0, thus z+y=0 and x=z-y=0) then |x|=z+y. But, if (z=2 and y=1, thus z+y=3 and x=z-y=1) then |x|$$\neq$$z+y.

statement-2: Insufficient as it doesn't give any info on y and z. Example, x=-3, z=-1, y=-2, thus |x|$$\neq$$z+y OR x=-3, z=1, y=2, thus |x|=z+y.

1+2: Insufficient.
Here, we know that, x=z-y and x<0,
when z=1 and y=2 then x = z-y=-1, and |x|$$\neq$$=y+z
but when z=0, y=1 then x=z-y=-1, and |x| = y+z
Intern
Joined: 03 Jan 2017
Posts: 23
GMAT 1: 680 Q49 V34
Re: Is |x| = y + z?  [#permalink]

### Show Tags

30 Apr 2017, 06:33

since abs(x)>=0, the question is asking is y+z>=0

Statement 1 says that Y=Z-X. This means that Y+Z=2Z-X. We don't have specific values for Z or X so not sufficient

Statement 2 says x>0. This alone means nothing. Insufficient.

Together x>0 and the question is whether 2Z-X>0. We have no indication of the direction of Z, so insufficient together.
Manager
Joined: 02 Feb 2016
Posts: 88
GMAT 1: 690 Q43 V41
Re: Is |x| = y + z?  [#permalink]

### Show Tags

25 Jul 2017, 15:36
For statement (1) we derive that

x+y = z

-x = y - z

When x is negative, y-z>0 and when x is positive, y-z<0 .. Knowing that y-z would be greater or less than 0 is insufficient to give us a similar indication for y+z ..

My question is whether this is a correct understanding of the information and can it be universally applied for two variables getting subtracted and added?
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3629
Re: Is |x| = y + z?  [#permalink]

### Show Tags

28 Jul 2017, 00:46
TheMastermind wrote:
For statement (1) we derive that

x+y = z

-x = y - z

When x is negative, y-z>0 and when x is positive, y-z<0 .. Knowing that y-z would be greater or less than 0 is insufficient to give us a similar indication for y+z ..

My question is whether this is a correct understanding of the information and can it be universally applied for two variables getting subtracted and added?

Hi TheMastermind ,

Yeah, this is another way to approach such questions.

Since you don't have any information about the sign of (y-z), you cannot conclude anything for y+z.

This is universally accepted concept and is not specific to this question.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Re: Is |x| = y + z?   [#permalink] 28 Jul 2017, 00:46
Display posts from previous: Sort by