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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
17 Sep 2010, 14:58

4

This post received KUDOS

Expert's post

8

This post was BOOKMARKED

This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\). In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\). In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.

So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Hi, rgtiwari Draw a number line and put 0 in the middle of it. now look at the data you are given. zy<xy<0. we don't know if y is positive or negative. if y>0 than z is on the left of x which is on the left of zero => z<x and both z & x are originally negative. the opposite if y<0, x will be on the right of zero and z will be on the right of x. => z>x. and both are originally positive. in both cases it seems that the equation is correct. but don't bother to check that just look at the extra data and continue from there. If you find it hard to understand with variables just use numbers instead. now let's look at (1) it tells you that z<x so we know that this is the first case only => the equality is definitely correct (just use numbers that maintain the data in the first case) - Sufficient. (2) it tells you that y>0. again we are at the first case. - Sufficient.

pay attention that this is not a coincidence that the extra data given leads you in (1) and (2) to the same conclusion. if it doesn't you should suspect whether it's D or not.

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
20 Jun 2012, 04:05

3

This post received KUDOS

Expert's post

rgtiwari wrote:

If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x (2) y > 0

You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'.

zy < xy < 0 implies both 'zy' and 'xy' are negative and zy is more negative i.e. has greater absolute value as compared to xy. Since y will be equal in both, z will have a greater absolute value as compared to x.

When will zy and xy both be negative? In 2 cases: Case 1: When y is positive and z and x are both negative. Case 2: When y is negative and z and x are both positive.

Question: Is | x - z | + |x| = |z| ? Is | x - z | = |z| - |x| ? Is | z - x | = |z| - |x| ? (Since | x - z | = | z - x |) We re-write the question only for better understanding.

Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign. In case both have the same sign, they get subtracted on both sides so you get the same answer. In case they have opposite signs, they get added on LHS and subtracted on RHS and hence the equality doesn't hold.

So if we can figure whether both x and z have the same sign, we can answer the question.

As we saw above, in both case 1 and case 2, x and z must have the same sign. This implies that the equality must hold and you don't actually need the statements to answer the question. You can answer it without the statements (this shouldn't happen in actual GMAT). Hence answer must be (D). _________________

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
17 Sep 2012, 23:44

2

This post received KUDOS

rgtiwari wrote:

If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x (2) y > 0

Since zy < 0 and xy < 0, both z and x have opposite sign to y, so they must be either both positive or both negative. In other words, we know that xz > 0.

(1) Given that z < x, when both z and x are negative, |z - x| + |x| = -z + x + (-x) = -z = |z| TRUE z and x cannot be both positive, because then y would be negative, and from zy < xy we would obtain that z > x. Sufficient.

(2) Knowing that y > 0, we can deduce that both z and x are negative. In addition, from zy < xy it follows that z < x, and we are in the same case as above. Sufficient.

Answer D _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
20 Dec 2012, 19:50

2

This post received KUDOS

Expert's post

eaakbari wrote:

If | z - x |= |z| - |x| assuming x & z have same sign | x - z |= |z| - |x| ; Since | x - z | = | z - x |

Implies |z| - |x| = |x| - |z| which is defn not true z = 1 , x = 2 Plugging, we get - 1 = 1 ?!?

Have I misunderstood something?

Before discussing this part, I have discussed in my post that absolute value of z must be greater than absolute value of x. If absolute value of z is not greater than absolute value of x, then | z - x |= |z| - |x| does not hold when x and z have the same sign.

Since |z| must be greater than |x|, | x - z | = |x| - |z| does not hold. _________________

Re: If zy<xy<0 is |x-z| + |x| = |z|? 1. z<x>0 2. [#permalink]
17 Sep 2012, 14:16

1

This post received KUDOS

successstory wrote:

If zy<xy<0 is |x-z| + |x| = |z|?

1. z<x>0 2. y>0

answer d.

why not a?

The question surprisingly does not require either statements for it to be true.

|x-z| + |x| = |z| can be rearranged as |x-z| = |z|-|x|. Now since we have an equal sign( opposed to an inequality, in which we would have to check both sides to make sure they are both positive or both negative to square (and flip)), we square both sides to get (|x-z|)^2 = (|z|-|x|)^2 which yields ===> xz=|x||z|

So our question becomes: Is xz=|x||z|?

Well this can only be true if (x>0 and z>0) OR (x<0 and z<0). In other words x and z must both be the same sign for the above statement to be true.

Now we are given zy<xy<0 as a fact. Two cases arise (+)(-)<(+)(-)<0 or (-)(+)<(-)(+)<0. Notice in both cases x and z are always the same sign!!!!! This statement is true from the gecko. Hence whatever unnecessary statement GMAC tells us will be sufficient. This is an usual problem you wont see again.

Re: Absolute values [#permalink]
26 Nov 2012, 17:54

1

This post received KUDOS

Is this really a 600 level question? Given its time consuming nature, seems more like a 750 level one.

Bunuel wrote:

This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happen then the answer should be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\). In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\). In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.

So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
08 Feb 2013, 11:18

1

This post received KUDOS

The question is not good. The target question "If zy < xy < 0, is | x - z | + |x| = |z|?" tells us zy<xy<0, that is, z and x have the same sign, Thus, target question could be rephrased as "| x - z | = |z|-|x| ?"=> "|z|>|x| ?" The condition zy<xy<0 could be rephrased as |zy|>|xy|>0 => |z|>|x| , which is already enough to solve the question.

if zy<xy<0 is Ix-zI+IxI=IzI [#permalink]
15 May 2013, 05:30

1

This post received KUDOS

from given

y(z-x) < 0 thus z is not = x and x is not equal to zero

if we square the 2 sides of the question

we get

x^2 + z^2 - 2xz +2x^2 - 2xz +x^2 = z^2 this boiles down to is 4x ( x-z) = 0 ? the answer is yes if x = 0 or x=z and no if we can know for sure that neother x=z nor x = 0

and this is given in the question stem.... neither givens are needed ..........as the answer is for sure NO

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
18 Jun 2014, 09:13

1

This post received KUDOS

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. _________________

Re: If zy < xy < 0, is | x - z | + |x| = |z|? [#permalink]
19 Jun 2015, 12:53

1

This post received KUDOS

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. _________________

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...