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

 It is currently 19 Feb 2019, 19:13

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

Author Message
TAGS:

Hide Tags

Intern
Joined: 06 Oct 2014
Posts: 10
If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

Show Tags

Updated on: 30 Nov 2014, 04:58
2
4
00:00

Difficulty:

25% (medium)

Question Stats:

82% (02:17) correct 18% (02:39) wrong based on 159 sessions

HideShow timer Statistics

If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

A. -10
B. -5
C. -4
D. 3
E. 7

Attachments

Screen Shot 2014-11-29 at 7.09.16 PM.png [ 15.14 KiB | Viewed 4006 times ]

Originally posted by FTS185 on 29 Nov 2014, 18:10.
Last edited by Bunuel on 30 Nov 2014, 04:58, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

Show Tags

30 Nov 2014, 04:58
2
FTS185 wrote:
If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

A. -10
B. -5
C. -4
D. 3
E. 7

$$2^y = 4^{(5x + 3)}$$ --> $$2^y = 2^{2(5x + 3)}$$ --> $$y = 2(5x + 3)$$;

$$3^{(x - 7)} = 9^y$$ --> $$3^{(x - 7)} = 3^{2y}$$ --> $$x-7=2y$$.

From above $$x = -1$$ and $$y=-4$$ --> $$x +y = -5$$.

_________________
Manager
Joined: 21 Sep 2012
Posts: 213
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

Show Tags

30 Nov 2014, 05:22
1
2^y = 4^(5x + 3)
2^y=2^2(5x+3)
y=10x+6 ........... 1

3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2

put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1

therefore, y= -10+6
y=-4

x+y= -1-4= -5

Ans - B
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1821
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

Show Tags

30 Nov 2014, 23:45
2
$$2^y = 4^{(5x + 3)}$$

$$2^y = 2^{2(5x+3)}$$

y = 10x+6 ........... (1)

$$3^{(x - 7)} = 9^y$$

$$3^{(x-7)}=3^{2y}$$

x-7 = 2y ............. (2)

x-7 = 2*(10x+6)

x = -1 & y = -4

x+y = -1 -4 = -5

_________________

Kindly press "+1 Kudos" to appreciate

Non-Human User
Joined: 09 Sep 2013
Posts: 9855
Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

Show Tags

21 Oct 2018, 23:33
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^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?   [#permalink] 21 Oct 2018, 23:33
Display posts from previous: Sort by