• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Is PQ > 1?

This topic has 2 expert replies and 0 member replies

Is PQ > 1?

Post
Is PQ > 1?

(1) P^Q = 1
(2) Q = -1

The OA is C.

I don't understand why both statements together are sufficient to solve this DS question. Experts, can you help me please?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
497 members
Upvotes:
2867
GMAT Score:
800
Top Reply
Post
Hi M7MBA,

We're asked if (P)(Q) > 1. This is a YES/NO question. We can solve it by TESTing VALUES and/or by using Number Property Rules.

1) P^Q = 1

With the equation in Fact 1, we know that one of the following must be occurring:
A) P = 1 and Q is ANY value
B) P = ANY value and Q = 0

With the first example, the product (P)(Q) could be greater than 1 (a YES answer), equal to 1 (a NO answer) or less than 1 (also a NO answer).
With the second example, the product (P)(Q) will always be 0, so the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) Q = -1

Fact 2 tells us nothing about the value of P, so there's no way to answer the question.
Fact 2 is INSUFFICIENT.

Combined, we know...
P^Q = 1
Q = -1
So (P)^(-1) = 1. The only solution to this equation is P=1, so (1)(-1) = -1 and the answer to the question is ALWAYS NO.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2666 messages
Followed by:
125 members
Upvotes:
1153
GMAT Score:
770
Post
M7MBA wrote:
Is PQ > 1?

(1) P^Q = 1
(2) Q = -1

The OA is C.

I don't understand why both statements together are sufficient to solve this DS question. Experts, can you help me please?
Statement 1:
Case 1: P = 1; Q = 1. PQ = 1, and so is not greater than 1. The answer is NO.
Case 2: P =1; Q = 50. PQ = 50, so is greater than 1. The answer is YES.
Because we can answer YES or NO, this statement alone is not sufficient.

Statement 2: Nothing about P, so not sufficient.

Together, Now we know P^(-1) = 1. The only way that can happen is if P = 1. If P =1 and Q= -1, then PQ = -1, and the answer to the question is a definitive NO. The statements together are sufficient. The answer is C

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 Ian Stewart 44 first replies
2 Jay@ManhattanReview 35 first replies
3 Brent@GMATPrepNow 34 first replies
4 Scott@TargetTestPrep 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

129 posts
2 image description Max@Math Revolution

Math Revolution

89 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

50 posts
5 image description Jay@ManhattanReview

Manhattan Review

35 posts
See More Top Beat The GMAT Experts