GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2018, 00:55

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

Events & Promotions

Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

Author Message
TAGS:

Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 10
If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

10 May 2012, 07:04
4
00:00

Difficulty:

5% (low)

Question Stats:

91% (01:18) correct 9% (01:49) wrong based on 257 sessions

HideShow timer Statistics

If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

A. (1,2)
B. (2,1)
C. (1,1)
D. (2,2)
E. (1,3)

I understand how to cancel out things for the first half of the problem. For the second half, GMATPrep v2 says that (3^2x)(3^y) = 3^4 becomes 32x + y = 34. Can somebody explain how that happens?
Math Expert
Joined: 02 Sep 2009
Posts: 50621
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

10 May 2012, 07:09
1
RyanP wrote:
If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

A. (1,2)
B. (2,1)
C. (1,1)
D. (2,2)
E. (1,3)

I understand how to cancel out things for the first half of the problem. For the second half, GMATPrep v2 says that (3^2x)(3^y) = 3^4 becomes 32x + y = 34. Can somebody explain how that happens?

$$2^x*2^y=8$$ --> $$2^{x+y}=2^3$$ --> $$x+y=3$$;
$$9^x*3^y=81$$ --> $$3^{2x}*3^y=3^4$$ --> $$3^{2x+y}=3^4$$ --> $$2x+y=4$$;

Solving: $$x+y=3$$ and $$2x+y=4$$ we get $$x=1$$ and $$y=2$$.

Hope it's clear.
_________________
Intern
Joined: 07 Jan 2011
Posts: 15
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

11 May 2012, 09:03
1
you could simply plug in answer choices into the equations and see which one is equal...
Intern
Joined: 24 Apr 2013
Posts: 49
Schools: Duke '16
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

28 May 2013, 15:44
If (2 to the power of X)(2 to the power of Y) and (9 to the power of X) (3 to the power of Y) = 81 then (X,Y) =

(1,2)

(2,1)

(1,1)

(2,2)

(1,3)
Math Expert
Joined: 02 Sep 2009
Posts: 50621
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

28 May 2013, 15:48
If (2 to the power of X)(2 to the power of Y) and (9 to the power of X) (3 to the power of Y) = 81 then (X,Y) =

(1,2)

(2,1)

(1,1)

(2,2)

(1,3)

Merging similar topics. Please refer to the solutions above.
_________________
Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

29 May 2013, 01:52
clicker wrote:
you could simply plug in answer choices into the equations and see which one is equal...

I think the plug-in method works best in the actual exam when you're fighting against the clock, or when you've exhausted all possible angles of attack on a notoriously difficult problem. But during preparation, I believe it is essential to understand how and why the concept work to solve these questions.

To solve this question you should be familiar with the following rules :

- $$a^x * a^y = a^(x+y)$$ (1) (notice that for this rule to work, we must have the same base, as in "a")
- $$(a^x)^y = a^(x*y)$$ (2)
- $$a^x = a^y$$ therefore $$x = y$$ (3) (same as with rule n°1, we need to have the same base)

Considering our problem, we have :

$$2^x*2^y = 8$$ which, according to (1) will yield $$2^(x+y) = 8 = 2^3$$ which, according to (3) will yield : $$x + y = 3$$
$$9^x*3^y = 81$$
Since $$9 = 3^2$$, then the above equation becomes : $$(3^2)^x*3^y = 81$$. According to (2), we can write : $$3^(2*x)*3^y = 81$$ which, according to (1) will yield $$3^(2x+y) = 81 = 3^4$$, which according to (3), will yield : $$2x + y = 4$$

We end up with a linear system of two equations :
$$x + y = 3$$
$$2x + y = 4$$

The solution of which is x = 1 and y = 2. Which is answer choice A.

Hope that helped
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4212
Location: India
GPA: 3.5
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

16 Oct 2016, 10:34
RyanP wrote:
If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

A. (1,2)
B. (2,1)
C. (1,1)
D. (2,2)
E. (1,3)

I understand how to cancel out things for the first half of the problem. For the second half, GMATPrep v2 says that (3^2x)(3^y) = 3^4 becomes 32x + y = 34. Can somebody explain how that happens?

$$(2^x) (2^y) = 8$$

Or, $$2^{ x + y } = 2^3$$

So, $$x + y = 3$$-------------->(I)

$$(9^x)(3^y) = 81$$

Or, $$3^{2x + y } =3^4$$

So, $$2x + y = 4$$----------->(II)

Combine (I) and (II)

$$2x + 2y = 6$$
$$2x + y = 4$$

Solve for $$y$$

$$y = 2$$

Plug in y = 2 in ( I)

$$x + y = 3$$

Or, $$x + 2 = 3$$

So, $$x = 1$$

Hence (x , y ) = ( 1 , 2 )

Thus answer will be (A) (1,2)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Director
Joined: 02 Sep 2016
Posts: 688
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

22 Jun 2017, 05:54
If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

If base is same, we add powers.
So,
x+y= 3 (3 because 2^3=8 and we are comparing/equating powers)
2x+y= 4

Let's subtract the two equations:
2x+y=4
-x-y=-3

x= 1
and thus y=2

A. (1,2)
B. (2,1)
C. (1,1)
D. (2,2)
E. (1,3)
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Non-Human User
Joined: 09 Sep 2013
Posts: 8794
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:  [#permalink]

Show Tags

05 Sep 2018, 12:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals: &nbs [#permalink] 05 Sep 2018, 12:05
Display posts from previous: Sort by