• 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

If x^y = 1 then what is the

This topic has 2 expert replies and 0 member replies

GMAT/MBA Expert

If x^y = 1 then what is the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



If x^y = 1, then what is the value of x?

(1) x < 0
(2) y is even integer

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
Brent@GMATPrepNow wrote:
If x^y = 1, then what is the value of x?

(1) x < 0
(2) y is even integer
\[{x^y} = 1\]
\[? = x\]

Let´s ALGEBRAICALLY BIFURCATE statements (1) and (2) together, to be "shielded" that the right answer is __(E)____ :
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 1,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = - 1 \hfill \\
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 2,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = - 2 \hfill \\
\end{gathered} \right.\,\,\,\,\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Brent@GMATPrepNow wrote:
If x^y = 1, then what is the value of x?

(1) x < 0
(2) y is even integer
Target question: What is the value of x?

Given: x^y = 1
If x^y = 1, then there are 3 possible cases:
case i: x = 1, and y = any value (e.g., 1^9 = 1)
case ii: x = -1, and y = an even integer (e.g., (-1)^4 = 1)
case iii: x = any non-zero value, and y = 0 (e.g., 7^0 = 1)


Statement 1: x < 0
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is even integer
Let's TEST some values.

PRO-TIP: When testing values, always check to see if you can reuse previous values.
In this case, we can reuse BOTH cases:
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Brent@GMATPrepNow 68 first replies
2 fskilnik@GMATH 56 first replies
3 Jay@ManhattanReview 39 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 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 fskilnik@GMATH

GMATH Teacher

130 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 image description Max@Math Revolution

Math Revolution

84 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

79 posts
5 image description Jay@ManhattanReview

Manhattan Review

76 posts
See More Top Beat The GMAT Experts