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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Is |x| = y-z? 1)x+y=z 2) x < 0 |x| = -x or x. If -x = [#permalink]
11 Sep 2004, 01:09

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

Is |x| = y-z?

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

|x| = -x or x.

If -x = y-z. then x+y = z
If x = y-z, then y-x = z

So from 1) x+y = z, so -x = y-z and |x| must be equals to y - z. So 1) is sufficient.

From 2) all we know is x is less than 0. Nothing about y or z is given. So 2) is insufficient.

OA is not my answer (which is A). What do you think of my working ? I'm having the thought that satisfying x+y=z OR y-x=z is sufficient to say if |x| = y-z.

If -x = y-z. then x+y = z If x = y-z, then y-x = z

So from 1) x+y = z, so -x = y-z and |x| must be equals to y - z. So 1) is sufficient.

From 2) all we know is x is less than 0. Nothing about y or z is given. So 2) is insufficient.

OA is not my answer (which is A). What do you think of my working ? I'm having the thought that satisfying x+y=z OR y-x=z is sufficient to say if |x| = y-z.

From 1 , one get x=z-y. If x is +ve then, it is z-y; with x negative, it is y-z
From 2 , you get x is negative, so C.
Let me know what do u feel.
S

I am a little confused when it got to |x| = -x = y-z. How can an absolute value of x be equals to its negative value ? Absolute values, I thought, have no negatives.

From 1 x = z-y
the value of x will depend on the magnitude of both z and y. if z> Y
then we get x to be positive and x = Z-Y. Iand abs(X) = y -z, right?

Now if Z < Y then X = - (z-y). If we take the absolute value, we get
abs(x) = abs(-(z-y)) = z -y, right. so A is sufficient.

I am a little confused when it got to |x| = -x = y-z. How can an absolute value of x be equals to its negative value ? Absolute values, I thought, have no negatives.

You are right and wrong.
Absolute values have no sign. So |x| is always postive and represents the magnitude of x.
But in this problem, we are talking about x. x, the actual number, does have sign apart from magnitude.

From statement I alone, you cannot say "Sufficient". I is sufficient if the number x is proved to be negative, which is given in statement II. Hence C. The problem with your approach is that you missed the OR part.

|x| = -x or x.

If -x = y-z. then x+y = z
OR
If x = y-z, then y-x = z

So from 1) x+y = z, so -x = y-z and x must be equals to y - z. So (1) is sufficient if x is negative. Nothing is known about the if x is positive. Insufficient.

From 2) all we know is x is less than 0. Insufficient.

Together (2) says that x is negative and 1 proves the negative part of stem. Sufficient

Hello, I think you are missing something here. wht you shd know is that the value of x is dependent on z and Y for instance let say z = 2 and y = 5
then
From statement one, X = 5-2 = 3, abs(x) = 3
Now flip it around and assume that y = 2 and Z = 5
then x = 2 - 5 = -3, abs(x) = 3.

So why do you say A is not sufficient

Now consider it this way, abs(x) could mean that x is positive or negative.
if x is positive
then we have
from one we have
X = y -z and abs(x) = abs(y-z) and abs(x) = y -z)
If X <0,
then from one it would mean
-x = z-y
X = -(z-y), take the absolute value of x and you get z-y.
meaning A is sufficient.

I don't think you need B to conclude that abs(x) will always be equal to
y -z or z - y.