BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT Prep Math zy < xy < 0 |x-z| + |x| = |z|

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Wed Mar 25, 2009 4:50 am

Proof_or so I think!

by manjithmanohar » Wed Mar 25, 2009 5:21 am
The basic condition for the equation |x-z| + |x| = |z| to be true is that
|z| > |x|

The inequality zy < xy < 0
further implies that |z| > |x| where the y value could be both +/ - respectively to maintain the inequality. (I hope I don't need to elaborate this part)

So considering the answers:

1. z < x (if it is considered with the inequality both z and x are negative and that y is positive.) so proves |z| > |x|, hence true.
2. y < 0 (when fit into the inequality proves that again |z| > |x|) so true.

Answer most definitely is D.

Please feel free to discuss this! :D
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Wed Mar 25, 2009 7:36 am
I posted a solution to this to another forum, so I'll just paste that here:

_______________

This is one of the strangest questions in GMATPrep, since you don't need either of the statements to answer the question. That's not supposed to happen on a GMAT DS question, which makes me wonder whether there was an error in the question design. In any case, we're given:

zy < xy < 0

Rewrite this as three inequalities:

(1) xy < 0
(2) zy < 0
(3) zy < xy

From (1), we have two possibilities:

(A) x is positive, and y is negative. Then, from (2), z is positive, and from (3), dividing by y and reversing the inequality because y is negative, we have x < z. So it may be that y < 0 < x < z .

(B) x is negative and y is positive. Then, from (2), z is negative, and from (3), dividing by y, we have z < x. So it may be that z < x < 0 < y .

Those are the only two possibilities here. Draw the number line in each case:

(A)

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

(B)

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


In either case, we can see that the distance from z to zero is equal to the sum of the distance from x to zero and the distance from x to z. That is, in either case, |z| = |x| + |x - z|. So we don't need any additional information to be sure that the answer to the question is yes - neither of the statements is required here.

I suppose that makes the answer 'D', though it's the only question I know of in any official GMAT material (and I've seen pretty much every question) where the statements aren't needed to answer the question given.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

Re: Proof_or so I think!

by bluementor » Wed Mar 25, 2009 9:10 am
manjithmanohar wrote: 1. z < x (if it is considered with the inequality both z and x are negative and that y is positive.) so proves |z| > |x|, hence true.
2. y < 0 (when fit into the inequality proves that again |z| > |x|) so true.
I thought DS statements should never contradict each other. You are getting y>0 in the first statement, and this clearly contradicts statement 2.

As Ian mentions in his post, this is a strange question.

-BM-
Top
User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: Proof_or so I think!

by Ian Stewart » Wed Mar 25, 2009 9:25 am
bluementor wrote:
manjithmanohar wrote: 1. z < x (if it is considered with the inequality both z and x are negative and that y is positive.) so proves |z| > |x|, hence true.
2. y < 0 (when fit into the inequality proves that again |z| > |x|) so true.
I thought DS statements should never contradict each other. You are getting y>0 in the first statement, and this clearly contradicts statement 2.

As Ian mentions in his post, this is a strange question.

-BM-
Nicely spotted - that's a typo in the original post, and in the real version of the question, Statement 2 reads "y > 0". The question is from GMATPrep; there's a screenshot of the question here:

gmatclub.com/forum/t70195-modulus-gmat-prep
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Master | Next Rank: 500 Posts
Posts: 148
Joined: Wed Jun 03, 2009 8:04 pm
Thanked: 18 times
Followed by:1 members

by ghacker » Sun Jun 14, 2009 7:48 am
This is a very simple question



Answer is D
Top
Master | Next Rank: 500 Posts
Posts: 122
Joined: Fri May 22, 2009 10:38 pm
Thanked: 8 times
GMAT Score:700

by rah_pandey » Wed Jun 17, 2009 2:00 am
Ian is right that none of the condition is needed to give the answer to the question. The equality is true under all circumstances
Top
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Mon Oct 26, 2009 8:28 am

by r321 » Mon Feb 28, 2011 12:29 pm
Ian Stewart wrote:I posted a solution to this to another forum, so I'll just paste that here:

_______________

This is one of the strangest questions in GMATPrep, since you don't need either of the statements to answer the question. That's not supposed to happen on a GMAT DS question, which makes me wonder whether there was an error in the question design. In any case, we're given:

zy < xy < 0

Rewrite this as three inequalities:

(1) xy < 0
(2) zy < 0
(3) zy < xy

From (1), we have two possibilities:

(A) x is positive, and y is negative. Then, from (2), z is positive, and from (3), dividing by y and reversing the inequality because y is negative, we have x < z. So it may be that y < 0 < x < z .

(B) x is negative and y is positive. Then, from (2), z is negative, and from (3), dividing by y, we have z < x. So it may be that z < x < 0 < y .

Those are the only two possibilities here. Draw the number line in each case:

(A)

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

(B)

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


In either case, we can see that the distance from z to zero is equal to the sum of the distance from x to zero and the distance from x to z. That is, in either case, |z| = |x| + |x - z|. So we don't need any additional information to be sure that the answer to the question is yes - neither of the statements is required here.

I suppose that makes the answer 'D', though it's the only question I know of in any official GMAT material (and I've seen pretty much every question) where the statements aren't needed to answer the question given.
I just got this question on my prep test today and spent about 10 minutes after the test trying to figure out why I would need either of the statements to answer the question stem...until, of course, i found this post (and others like it - https://www.manhattangmat.com/forums/pos ... tml#p30742)

Makes me wonder though - if all the gmat prep software questions are retired questions from the official test, doesn't that mean that the official GMAT at one point contained this (clearly flawed) question!

And, I downloaded the prep software only in January '11 - seems like they still haven't realised that this question is flawed..
Top
Post new topic Post Reply
• Page 1 of 1