 It is currently Mon Sep 16, 2019 5:25 am

 All times are UTC - 5 hours [ DST ]  Page 1 of 2 [ 12 posts ] Go to page 1, 2  Next
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Algebra (Data Sufficiency) Posted: Fri Feb 24, 2012 7:12 pm Joined: Sun May 30, 2010 3:15 am
Posts: 424
Is (x – 4)(x – 3)(x + 2)(x + 1) > 0 ?
(1) 3 > x
(2) x > -1

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) The expression (x – 4)(x – 3)(x + 2)(x + 1) is composed of four factors. It will equal 0 if at least one of the factors is 0. It will be positive if all the four factors are positive, if all the four factors are negative, or if two of them are negative and the other two are positive. Otherwise the epxression will be negative.

Statement (1), 3 > x, implies that the factors (x – 4) and (x – 3) are negative. The signs of the other two factors, (x + 2) and (x + 1), are not defined. E.g. they both can be positive if x = 1. Or one of them can equal 0 if x = -1 or x = -2. Or (x + 2) can be positive and (x + 1) can be negative if x = -1.5, etc. Therefore the original expression can be positive, negative or 0 and we can NOT give a definite answer to the original question. Statement (1) by itself is NOT sufficient.

Statement (2), x > -1, implies that the factors (x + 2) and (x + 1) are positive. The signs of the other two factors, (x – 4) and (x – 3) , are not defined. E.g. they both can be positive if x = 5. Or one of them can equal 0 if x = 3 or x = 4. Or (x – 3) can be positive and (x – 4) can be negative if x = 3.5, etc. Therefore the original expression can be positive, negative or 0 and we can NOT give a definite answer to the original question. Statement (2) by itself is NOT sufficient.

If we use the both statements together, statement (1) implies that factors (x – 4) and (x – 3) are negative. Statement (2) implies that factors (x + 2) and (x + 1) are positive. Therefore the original expression must be positive (2 negative factors × 2 positive factors). The both statements taken together are sufficient to answer the question. The correct answer is C.

Alternative method:
You may solve the original inequality first and then compare the solution with the inequality (1), inequality (2) and a system of inequalities (1) and (2) using the number line.
----------

Between -1 & 3 the expression acquires negative as well as positive values.

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Feb 24, 2012 7:23 pm Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Mar 23, 2012 3:52 pm Joined: Sun May 30, 2010 3:15 am
Posts: 424
1st won't work - check for x = 3.5 and 7 - they will give opposite signs.
2nd won't work - check for x = 1 and 5 - they will give opposite sings.

Combining the both won't work - check for x = 1 and -1.5 - they again give opposite signs.

Hence the answer is E.

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Mar 23, 2012 4:24 pm Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Mar 24, 2012 2:15 am Joined: Sat Mar 24, 2012 2:10 am
Posts: 1
1st won't work - check for x=1 and -1.5 - they will give opp.signs and satisfies x<3
2nd won't work - check for x=3.5 and 5 - they will give opp.sings and satisfies x > -1

combining both won't work- check for x=1 and -1.5 - they again give opp.signs and satisfies -1<x<3

hence ans is E

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Mar 24, 2012 2:32 pm Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Mon May 07, 2012 4:36 am Joined: Sun May 30, 2010 3:15 am
Posts: 424
For x = -3/2 the answer is -ive while for x = 0 it will be +ive. Thus even if we use both A and B, the value for the expression is not certain.
For range -1 to -2 the expression is -ive
For range -2 to -3 the expression is +ive

Thus answer should be E

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Mon May 07, 2012 6:46 am Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Jul 14, 2012 4:07 pm Joined: Sun May 30, 2010 3:15 am
Posts: 424
Can you explain the alternative method in a little more detail.

Top Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Jul 14, 2012 4:31 pm Joined: Sun May 30, 2010 2:23 am
Posts: 498

 Attachments: intervals2.gif [1.92 KiB] Not downloaded yet intervals1.gif [1.79 KiB] Not downloaded yet
Top Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending  Page 1 of 2 [ 12 posts ] Go to page 1, 2  Next

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 3 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group