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

It is currently 14 Oct 2019, 03:43

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If x and y are integers and 72^x∗54^y=96, what is the value of x−y?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58313
If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 07 Mar 2017, 01:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (02:36) correct 32% (02:57) wrong based on 152 sessions

HideShow timer Statistics

Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 269
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 07 Mar 2017, 02:12
6
1
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


\(72^x∗54^y=96\)

\((3^2*2^3)^x∗(3^3*2)^y=2^5*3\)

\(3^{2x}*2^{3y}*3^{3y}*2^y=2^5*3\)

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

on solving 2x+3y=1 and 3x+y=5 we get x=2 and y=-1
so x-y = 2-(-1) =3

Hence option E is correct
Hit Kudos if you liked it 8-)
General Discussion
Intern
Intern
avatar
B
Joined: 30 Jan 2018
Posts: 13
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 21 Feb 2018, 14:20
1
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


72^x∗54^y=96 divide 6 at both side of the equation:
12^x*9^y=16 divide 3 at both side of the equation:
4^x*3^y=16/3
So x=2, y=-1
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1180
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 22 Feb 2018, 10:02
Missyy wrote:
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


72^x∗54^y=96 divide 6 at both side of the equation:
12^x*9^y=16 divide 3 at both side of the equation:

4^x*3^y=16/3
So x=2, y=-1


Hi Missyy

You cannot divide both sides of the exponents and use the quotients in a manner that you did.

for eg if we have \(6^2*9^2\) and as per you approach if I divide this by 3, then I should get \(2^2*3^2=36\)

but actually it will be \(\frac{6*6*9*9}{3}=972\).

Moreover the division is also wrong. \(72^x*54^y\) is one number but you are individually dividing both \(72^x\) & \(54^y\) by 6 individually. Had there been a + or - then individual division might be possible but in case of variable exponents it is incorrect
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 04 Feb 2019, 23:09
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


Be careful in such questions



\(72^x * 54^y = 96\)

Convert the above into their factors

[2^3 * 3^2]^x * [2*3^3]^y = 2^5 * 3^1
2^3x * 2^y * 3^2x * 3^3y = 2^5 * 3^1

3x + y = 5
2x + 3y = 1

Solve them to get x =2 & y =-1

E
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Manager
avatar
S
Joined: 22 Sep 2018
Posts: 240
If x and y are integers and 72^x∗54^y=96, what is the value of x−y?  [#permalink]

Show Tags

New post 05 Feb 2019, 16:01
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


My reasoning:

72 broken down into primes is \(2^3 * 3^2\) After multiplying x in we get \({2^3x} * 3^{2x}\)

54 broken down into primes is \(2 * 3^3\) After multiplying y in we get \(2^y * 3^{3y}\)

96 broken down into primes is \(2^5 * 3\)

Same base means you can add the exponents together so we get: \(2^{(3x+y)} * 3^{(2x+3y)}\)

We know \(2^{(3x+y)} = 2^5\) and \(3^{(2x+3y)} = 3^1\)

We can solve for x and y now which gives us 2 and -1 respectively. Subtract them and we get 3 (Choice E)
GMAT Club Bot
If x and y are integers and 72^x∗54^y=96, what is the value of x−y?   [#permalink] 05 Feb 2019, 16:01
Display posts from previous: Sort by

If x and y are integers and 72^x∗54^y=96, what is the value of x−y?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne