 It is currently 18 Oct 2019, 03:44 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. Which of the following is equal to..for all integers x and y  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 142

Kudos [?]: 2143 , given: 397

Which of the following is equal to..for all integers x and y [#permalink]
Expert's post 00:00

Question Stats: 85% (01:09) correct 14% (01:13) wrong based on 47 sessions
Which of the following is equal to $$\frac{2^{x-y}}{2^{x+y}}$$ for all integers $$x$$ and $$y$$ ?

A. $$4^{-x}$$

B. $$4^{-y}$$

C. $$2^{xy}$$

D. $$4^x$$

E. $$4^y$$

Practice Questions
Question: 10
Page: 83
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Last edited by Carcass on 08 Feb 2019, 11:25, edited 1 time in total.
Edited by Carcass GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 142

Kudos [?]: 2143  , given: 397

Re: Which of the following is equal to..for all integers x and y [#permalink]
1
KUDOS
Expert's post
Explanation

Simplifying the fraction $$\frac{2^x^-^y}{2^x^+^y}$$, yields $$\frac{2^x^-^y}{2^x^+^y}$$=$$2^-^2^y$$. The only answer choice with 2 as the base is Choice C, $$2^x^y$$, , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.

$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.

Thus the correct answer is Choice B.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GRE Instructor Joined: 10 Apr 2015
Posts: 2477
Followers: 83

Kudos [?]: 2483 , given: 34

Re: Which of the following is equal to..for all integers x and y [#permalink]
Expert's post
sandy wrote:
Which of the following is equal to $$\frac{2^x^-^y}{2^x^+^y}$$ for all integers x and y ?

A. $$4^-^x$$
B. $$4^-^y$$
C. $$2^x^y$$
D. $$4^x$$
E. $$4^y$$

Another approach is to use the INPUT-OUTPUT method.

Let x = 2 and y = 1

In this case, $$\frac{2^x^-^y}{2^x^+^y}$$ = $$\frac{2^1}{2^3}$$ = $$\frac{1}{4}$$
So, when the INPUT is x = 2 and y = 1, the OUTPUT is 1/4

The correct answer choice will be the one that has an OUTPUT of 1/4 when the INPUT is x = 2 and y = 1

A. $$4^-^x$$ = 4^(-2) = 1/16. ELIMINATE A.
B. $$4^-^y$$ = 4^(-1) = 1/4. KEEP B.
C. $$2^x^y$$ = 2^(2) = 4. ELIMINATE C.
D. $$4^x$$ = 4^(2) = 16. ELIMINATE D.
E. $$4^y$$ = 4^(1) = 4. ELIMINATE E.

[Reveal] Spoiler:
B

RELATED RESOURCES (videos)
- Variables in the Answer Choices - https://www.greenlighttestprep.com/modu ... /video/936
- Tips for the Algebraic Approach - https://www.greenlighttestprep.com/modu ... /video/937
- Tips for the Input-Output Approach - https://www.greenlighttestprep.com/modu ... /video/938

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails

Intern Joined: 18 Jul 2018
Posts: 6
Followers: 0

Kudos [?]: 1 , given: 2

Re: Which of the following is equal to..for all integers x and y [#permalink]
sandy wrote:
Explanation

Simplifying the fraction $$\frac{2^x^-^y}{2^x^+^y}$$, yields $$\frac{2^x^-^y}{2^x^+^y}$$=$$2^-^2^y$$. The only answer choice with 2 as the base is Choice C, $$2^x^y$$, , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.

$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.

Thus the correct answer is Choice B.

Can you please explain how you simplify that fraction? Director Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 44  , given: 1

Re: Which of the following is equal to..for all integers x and y [#permalink]
1
KUDOS
msawicka wrote:
sandy wrote:
Explanation

Simplifying the fraction $$\frac{2^x^-^y}{2^x^+^y}$$, yields $$\frac{2^x^-^y}{2^x^+^y}$$=$$2^-^2^y$$. The only answer choice with 2 as the base is Choice C, $$2^x^y$$, , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.

$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.

Thus the correct answer is Choice B.

Can you please explain how you simplify that fraction?

=$$\frac{2^x^-^y}{2^x^+^y}$$

=$$2^x^-^y^-^x^-^y$$

=$$2^-^2^y$$

now
$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.
Intern Joined: 07 May 2019
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 1

Re: Which of the following is equal to..for all integers x and y [#permalink]
AE wrote:
msawicka wrote:
sandy wrote:
Explanation

Simplifying the fraction $$\frac{2^x^-^y}{2^x^+^y}$$, yields $$\frac{2^x^-^y}{2^x^+^y}$$=$$2^-^2^y$$. The only answer choice with 2 as the base is Choice C, $$2^x^y$$, , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.

$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.

Thus the correct answer is Choice B.

Can you please explain how you simplify that fraction?

=$$\frac{2^x^-^y}{2^x^+^y}$$

=$$2^x^-^y^-^x^-^y$$

=$$2^-^2^y$$

now
$$2^-^2^y= \frac{1}{2^2^y}= 4^-^y$$.

What happens to the 2 on the bottom? I feel like I'm missing the step that allows us to put the exponents all on one line.
Founder  Joined: 18 Apr 2015
Posts: 8451
Followers: 165

Kudos [?]: 1819 , given: 7831

Re: Which of the following is equal to..for all integers x and y [#permalink]
Expert's post
It is a property of fraction and exponents.

The same base then you do have the two raised to the two exponents subtracted

Attachment: GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos Re: Which of the following is equal to..for all integers x and y   [#permalink] 07 May 2019, 11:19
Display posts from previous: Sort by

Which of the following is equal to..for all integers x and y  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.