If zy < xy < 0, is mod (x-z)....

[nehag84]

Hi...could someone pls explain how to solve this one..

If zy < xy < 0, is mod (x-z) + mod (x) = mod (z)

a) z < x
b) y > 0

OA is D.

This is a GMAT prep Q.

[Kweku.Amoako]

Hi,

this took me a while.

if mod(x-z) + mod(x) = mod(z) then we can re-arrange as

mod(x-z) = mod(z) - mod(x)

also zy < xy < 0

in other words

Case 1 : if y > 0 then z and x are both positive

and mod(x - z) = mod(z) - mod(x) only if mod(z) > mod(x) or z>x

case 2 : if y < 0 then both x and y are negative

and mod(x-z) = mod(z) - mod(x) only if z < x ( because eg the mod of -10 is greater than the mod of -4)

so in other words if we know the sign of y or how x relates z , then we will have enough information to answer "Yes" or "No"

1) z < x is same as case 2 so sufficient

2) y > 0 is same as case 1 so Sufficient

Good question...what question # is this ?

[nimish.tiwari]

Hi...could someone pls explain how to solve this one..

If zy < xy < 0, is mod (x-z) + mod (x) = mod (z)

a) z < x
b) y > 0

OA is D.

This is a GMAT prep Q.

Consider zy < xy < 0. Two possibilities arise:
(1) z & x are positive and y is negative. OR
(2) z & x are negative and y is positive.

Now take (1) above. Consider z, x and y as 3, 2 & -1 respectively (such that zy < xy < 0). But this contradicts with (a) above i.e. z < x.

So, y cannot be negative. So, (1) is not possible.

Now, consider (2) such hat z & x are negative and y is positive.
Lets assume that z, x and y are -3, -2 and 1 respectively (such that zy < xy < 0).
Also, in this case z < x (inline with (a) above).
Now, putting these values in eqn: mod (x-z) + mod (x) = mod (z)
==> mod (-2+3) + mod (-2) = mod (-3)
==> 1 + 2 = 3
Hence, the expression is correct and (a) is sufficient to answer.

Now, consider (b) y > 0. considering this with the given inequality of zy < xy < 0, we are back at what we did for (2) above. Hence, this would also be sufficient to answer.

Since, (a) and (b) are both ALONE sufficient to answer the question, D is the correct choice.

[RonPurewal]

heh, this problem.

believe it or not, it turns out that JUST THE PROBLEM STATEMENT IS ALREADY SUFFICIENT on this problem!

in other words, this problem is already "sufficient", even without EITHER of the two statements!

yes, you read that correctly.

proof:

* "zy < xy < 0" means that z and y have opposite signs, and x and y have opposite signs. therefore, x and z have the same sign.
furthermore, z must be farther away from zero than x (because the magnitude of zy is greater than the magnitude of xy).

therefore, there are only 2 possibilities (shown on number line):

y-------0-------x--------z

or

z-------x-------0-------y


now let's turn to the problem statement.

|x - z| is the distance between x and z.
|x| is the distance between 0 and x.
|z| is the distance between 0 and z.

using these interpretations, it's plain that |x - z| + |x| = |z| is ALREADY true for both of these statements.

neither of statements (1) and (2) is necessary.

technically, there's no answer choice that does this ("the problem statement is already sufficient"), although it's clear that you should pick (d) should this situation ever arise on the real exam.

it's problems like this that make me worry about the secrecy of the official test.

how recently did you get this problem? when did you download the software?
it's been in the software for at least a couple of years; i'm surprised they wouldn't have removed it by now.

[adiagr]

heh, this problem.

believe it or not, it turns out that JUST THE PROBLEM STATEMENT IS ALREADY SUFFICIENT on this problem!

in other words, this problem is already "sufficient", even without EITHER of the two statements!

yes, you read that correctly.

proof:

* "zy < xy < 0" means that z and y have opposite signs, and x and y have opposite signs. therefore, x and z have the same sign.
furthermore, z must be farther away from zero than x (because the magnitude of zy is greater than the magnitude of xy).

therefore, there are only 2 possibilities (shown on number line):

y-------0-------x--------z

or

z-------x-------0-------y


now let's turn to the problem statement.

|x - z| is the distance between x and z.
|x| is the distance between 0 and x.
|z| is the distance between 0 and z.

using these interpretations, it's plain that |x - z| + |x| = |z| is ALREADY true for both of these statements.

neither of statements (1) and (2) is necessary.

technically, there's no answer choice that does this ("the problem statement is already sufficient"), although it's clear that you should pick (d) should this situation ever arise on the real exam.

it's problems like this that make me worry about the secrecy of the official test.

how recently did you get this problem? when did you download the software?
it's been in the software for at least a couple of years; i'm surprised they wouldn't have removed it by now.

Ron , I got this problem on the GMAT prep on 2nd Jul 2010. I have a GMAT prep CD.

Aditya

[mschwrtz]

Aditya, is that the current CD? Was it sent recently, when you signed up for the test? Disappointing if so.

[debmalya.dutta]

If zy < xy < 0, is mod (x-z) + mod (x) = mod (z)

a) z < x
b) y > 0

using Statement 1 :
from the question , zy < xy
y(z-x)<0 ------- (A)
Now statement 1 tells me that (z-x)< 0 . This implies Y>0
So, if zy < xy < 0 and Y>0
This implies Z & X < 0
mod (x-z) + mod (x) = X-Z (since Z-X<0) + (-X) = -Z = |Z|

Using Statement 2 :
From (A), y(z-x)<0
Since from Statement 2 we know that y > 0
That implies (z-x)< 0 ..The subsequent reasoning is similar to that in Statement

[RonPurewal]

If zy < xy < 0, is mod (x-z) + mod (x) = mod (z)

a) z < x
b) y > 0

using Statement 1 :
from the question , zy < xy
y(z-x)<0 ------- (A)
Now statement 1 tells me that (z-x)< 0 . This implies Y>0
So, if zy < xy < 0 and Y>0
This implies Z & X < 0
mod (x-z) + mod (x) = X-Z (since Z-X<0) + (-X) = -Z = |Z|

Using Statement 2 :
From (A), y(z-x)<0
Since from Statement 2 we know that y > 0
That implies (z-x)< 0 ..The subsequent reasoning is similar to that in Statement

this looks ok, yes. but do note the reasoning above, in which you don't even need the statements; make sure you can also follow that reasoning, without either of the two statements.

[ldoolitt]

Sorry to bump a really old thread...

This is still on the most recent GMAT PREP software. I just saw it on mine. I arrived at the same conclusion Ron did above and was so confused that I sat there for a whole minute trying to figure out what I did wrong!

Anyway, my solution:

From zy < xy < 0, we know that y != 0. Use the case approach.

y>0 case
Dividing through by Y (since it is positive), yields

z < x < 0

Looking at the equation in question we note that since z and x are both negative, abs(z) = -z and abs(x) = -x. So we have

abs (x-z) - x = -z?
abs (x-z) = x - z?

This will be true of x-z > 0 or if x>z. But we already know from the given equation and the fact that y>0 that x>z. Thus if y>0 then the answer is YES.

y<0 case
Perform the flip steps. Dividing through by Y (since it is negative), yields

z > x > 0

Looking at the equation in question we note that since z and x are both positive, abs(z) = z and abs(x) = x. So we have

abs (x-z) x = z?
abs (x-z) = z - x?

This will be true of x-z < 0 or if z>x. But again we already know from the given equation and the fact that y<0 that z>x. Thus if y<0 then the answer is YES.

In either case the answer is YES.

[RonPurewal]

looks legit.

[jp.jprasanna]

heh, this problem.

believe it or not, it turns out that JUST THE PROBLEM STATEMENT IS ALREADY SUFFICIENT on this problem!

in other words, this problem is already "sufficient", even without EITHER of the two statements!

yes, you read that correctly.

proof:

* "zy < xy < 0" means that z and y have opposite signs, and x and y have opposite signs. therefore, x and z have the same sign.
furthermore, z must be farther away from zero than x (because the magnitude of zy is greater than the magnitude of xy).

therefore, there are only 2 possibilities (shown on number line):

y-------0-------x--------z

or

z-------x-------0-------y


now let's turn to the problem statement.

|x - z| is the distance between x and z.
|x| is the distance between 0 and x.
|z| is the distance between 0 and z.

using these interpretations, it's plain that |x - z| + |x| = |z| is ALREADY true for both of these statements.

neither of statements (1) and (2) is necessary.

technically, there's no answer choice that does this ("the problem statement is already sufficient"), although it's clear that you should pick (d) should this situation ever arise on the real exam.

it's problems like this that make me worry about the secrecy of the official test.

how recently did you get this problem? when did you download the software?
it's been in the software for at least a couple of years; i'm surprised they wouldn't have removed it by now.

Hi Ron - Thank you for the solution .... just one doubt here..

But there are other possibility as well right,

y = 5 , z =1 and x = 10 the y(z-x) < 0 is true

------- 0 ------ 1(z) ------- 5(y) ---------- 10(x)

but the question |x - z| + |x| = |z| becomes NO

Could you please let me know the flaw in my reasoning? In most of the problem I get the right ans solving algebraically but when try to validate my ans by choosing nos as in the case of this question I'm lost!

But for : y = 5 , z =1 and x = 10 the y(z-x) < 0 is true
but "zy < xy < 0" is NOT true...!

Cheers

[RonPurewal]

But there are other possibility as well right,

y = 5 , z =1 and x = 10

these numbers don't satisfy the conditions stipulated in the problem (zy < xy < 0) and are thus irrelevant.