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

Redeem

p>q, Is q negative?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members

p>q, Is q negative?

by VJesus12 » Thu Apr 12, 2018 9:16 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

p>q, Is q negative?

(1) pq + q^2 is positive
(2) (p^2)(q) + (p)(q^2) is positive

The OA is E.

How can I determine that the correct answer is the option E? May someone help me?
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

Senior | Next Rank: 100 Posts
Posts: 38
Joined: Mon Mar 19, 2018 6:26 am
Followed by:1 members

by Keith@ThePrincetonReview » Fri Apr 13, 2018 7:39 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

VJesus12 wrote:p>q, Is q negative?

(1) pq + q^2 is positive
(2) (p^2)(q) + (p)(q^2) is positive

The OA is E.

How can I determine that the correct answer is the option E? May someone help me?
This is a Yes/No question with variables in the question stem and in the statements, so you can Plug In values for p and q.

Statement (1) states that pq + q^2 > 0
Plug In p=2 and q=3, so that (2)(3) + (3)^2 > 0, and 6 + 9 > 0.
Since the inequality is true when q=3, q can be positive.
Try to prove the statement insufficient by showing that q can also be negative.
Plug In p=2 and q=-3, so that (2)(-3) + (-3)^2 > 0, and -6 + 9 > 0.
Since the inequality is true when q=-3, q can be negative.
Statement (1) is insufficient, so write down BCE.

Statement (2) states that (p^2)(q) + (p)(q^2) > 0
Factor p out of the expression on the left of the inequality sign, so that p(pq + q^2) > 0.
We know from Statement (1) that pq + q^2 > 0 can be true whether q is positive or negative.
Therefore, p(pq + q^2) > 0 can be true whether q is positive or negative.
Statement (2) is insufficient, so eliminate choice B.

The expression in Statement (2) is simply p times the expression in Statement (1), so the combination of the statements provides no additional information.
The correct answer is choice E.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Apr 14, 2018 2:56 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

VJesus12 wrote:p>q, Is q negative?

(1) pq + q^2 is positive
(2) (p^2)(q) + (p)(q^2) is positive
Statement 1:
Case 1: q=1
Substituting q=1 into pq + q² > 0, we get:
p(1) + 1² > 0
p > -1.
Since this case requires that p>-1, and the prompt requires that p>q, it's possible that p=2.
Thus, a valid combination for Statement 1 is p=2 and q=1, in which case the answer to the question stem is NO.

Case 2: q=-1
Substituting q=-1 into pq + q² > 0, we get:
p(-1) + (-1)² > 0
-p > -1.
p < 1.
Since this case requires that p<1, and the prompt requires that p>q, it's possible that p=1/2.
Thus, a valid combination for Statement 1 is p=1/2 and q=-1, in which case the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Test whether Case 1 (p=2 and q=1) satisfies p²q + pq² > 0:
2²(1) + 2(1²) > 0
6 > 0.
This works.
Thus, a valid combination for Statement 2 is p=2 and q=1, in which case the answer to the question stem is NO..

Test whether Case 2 (p=1/2 and q=-1) satisfies p²q + pq² > 0:
(1/2)²(-1) + (1/2)(-1)² > 0
-1/4 + 1/2 > 0
1/4 > 0.
This works.
Thus, a valid combination for Statement 2 is p=1/2 and q=-1, in which case the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statements combined:
Cases 1 and 2 satisfy both statements.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1