If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 23:35

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

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

Hide Tags

Intern
Joined: 09 Feb 2011
Posts: 11
Followers: 0

Kudos [?]: 72 [2] , given: 1

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

11 Feb 2011, 02:17
2
This post received
KUDOS
26
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

76% (02:08) correct 24% (01:11) wrong based on 477 sessions

HideShow timer Statistics

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Sep 2012, 13:15, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7103

Kudos [?]: 93597 [4] , given: 10579

Re: ps [#permalink]

Show Tags

11 Feb 2011, 04:13
4
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
alltimeacheiver wrote:
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

$$5^x-5^{x-3}=124*5^y$$ --> factor out $$5^{x-3}$$: $$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3}=5^y$$ --> bases are equal so we can equate the powers: $$y=x-3$$.

Answer: C.

alltimeacheiver format the questions correctly.
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 106 [3] , given: 161

Re: ps [#permalink]

Show Tags

18 Feb 2011, 11:17
3
This post received
KUDOS
u can also plug in x=3. makes it very simple.
_________________
Intern
Joined: 12 Dec 2011
Posts: 12
Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE: Management Consulting (Consulting)
Followers: 0

Kudos [?]: 19 [0], given: 5

Re: ps [#permalink]

Show Tags

20 Sep 2012, 13:05
Bunuel wrote:
alltimeacheiver wrote:
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

$$5^x-5^{x-3}=124*5^y$$ --> factor out $$5^{x-3}$$: $$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3}=5^y$$ --> bases are equal so we can equate the powers: $$y=x-3$$.

Answer: C.

alltimeacheiver format the questions correctly.

Hi Bunuel,
I', trying to understand your factorization, but I find some troubles when I have to factorize some value with exponent an expression like in the question (x-3 or x+4),
Could you explain me that or do you have a deck where I could dive into this argument?
Thank you in advance
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7103

Kudos [?]: 93597 [0], given: 10579

Re: ps [#permalink]

Show Tags

20 Sep 2012, 13:14
Expert's post
1
This post was
BOOKMARKED
mario1987 wrote:
Bunuel wrote:
alltimeacheiver wrote:
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

$$5^x-5^{x-3}=124*5^y$$ --> factor out $$5^{x-3}$$: $$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3}=5^y$$ --> bases are equal so we can equate the powers: $$y=x-3$$.

Answer: C.

alltimeacheiver format the questions correctly.

Hi Bunuel,
I', trying to understand your factorization, but I find some troubles when I have to factorize some value with exponent an expression like in the question (x-3 or x+4),
Could you explain me that or do you have a deck where I could dive into this argument?
Thank you in advance

$$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3+3}-5^{x-3}=124*5^y$$ --> $$5^{x}-5^{x-3}=124*5^y$$.

Theory: math-number-theory-88376.html

Practice:
tough-and-tricky-exponents-and-roots-questions-125956.html
tough-and-tricky-exponents-and-roots-questions-125967.html

Hope it helps.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 434 [2] , given: 11

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

12 Dec 2012, 18:52
2
This post received
KUDOS
1
This post was
BOOKMARKED
$${5^{x}}\frac{124}{125}=124(5^y)$$
$$5^{x}=5^{y+3}$$
$$x=y+3-->y=x-3$$

Answer: C
_________________

Impossible is nothing to God.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7130
Location: Pune, India
Followers: 2140

Kudos [?]: 13707 [9] , given: 222

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

13 Dec 2012, 02:25
9
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
vaivish1723 wrote:
5^x – 5^(x- 3) = (124)(5^y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

Oa is
[Reveal] Spoiler:
c

Finding one variable in terms of another is very simple. Assume a value for one and find the other. Then look for the option that works.

Say, x = 3 (so that x-3 becomes 0 and we are left with simple calculations)

$$5^3 - 5^{3- 3} = (124)(5^y)$$
$$1 = 5^y$$
y = 0

Now put x = 3 in the options and find out which option gives you y = 0. Only C does so answer is (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 24 Jan 2012 Posts: 10 Followers: 0 Kudos [?]: 132 [0], given: 3 Re: ps [#permalink] Show Tags 24 Sep 2013, 08:07 144144 wrote: u can also plug in x=3. makes it very simple. Hi, Can you please tell why you chose only 3 to substitute x with ? SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1937 [4] , given: 193 If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] Show Tags 26 Feb 2014, 19:47 4 This post received KUDOS 1 This post was BOOKMARKED $$5^x – 5^{(x- 3)} = 124*5^y$$ Re-write as $$5^x – 5^{(x- 3)} = (125 - 1 ) * 5^y$$ $$5^x – 5^{(x- 3)} = 125* 5^y - 5^y$$ $$5^x – 5^{(x- 3)} = 5^{(y+3)} - 5^y$$ LHS = RHS, so equating the powers y = x+3 ; Answer = C _________________ Kindly press "+1 Kudos" to appreciate GMAT Club Legend Joined: 09 Sep 2013 Posts: 13534 Followers: 577 Kudos [?]: 163 [0], given: 0 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] Show Tags 28 Mar 2015, 22:00 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. _________________ Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1782 Followers: 51 Kudos [?]: 393 [1] , given: 21 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] Show Tags 29 Mar 2015, 07:10 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED alltimeacheiver wrote: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? A. x B. x - 6 C. x - 3 D. 2x + 3 E. 2x + 6 Given that 5^x – 5^(x- 3) = 124*5^y So, 5^(x-3+3) - 5^(x- 3) = 124*5^y So, 5^(x-3) [5^3 - 1] = 124*5^y So, 5^(x-3)*124 = 124*5^y So, 5^(x-3) = 5^y So, x-3 = y Hence option (C). -- Optimus Prep's GMAT On Demand course for only$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring GMAT On Demand Course$299
Free Online Trial Hour

Intern
Joined: 21 Feb 2015
Posts: 28
Followers: 0

Kudos [?]: 5 [1] , given: 23

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

07 Aug 2015, 16:29
1
This post received
KUDOS
ok this is how you solve this

you have 5^x -5^x-3 = (124) (5^y)
step 1: 5^x (1-5^-3) =(124) (5^y)
Step 2: 5^x(1 - 1/5^3) = (124) (5^y)
Step 3: 5^x(1- 1/125) = (124) (5^y)
Step 4: 5^x (125-1)/125 = (124) (5^y)
Step 5: 5^x (124/125) = (124) (5^y)
Step 6: 5^x =[(124) (5^y) (125) ]/124
Step 7: 5^x = (125) (5^y)
Step 8: 5^x = 5^3 (5^y)
Step 9: x = 3 +y --> y = x -3
for explaining purposes I broke it down in to 9 steps. It should not take you more than 5 steps to solve this in term of y.
Ryerson (Ted Rogers) Thread Master
Joined: 27 Sep 2015
Posts: 63
Location: Canada
GMAT 1: 410 Q33 V13
WE: Management Consulting (Computer Software)
Followers: 4

Kudos [?]: 40 [0], given: 26

Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

19 Dec 2015, 12:57
Rookie124 wrote:
ok this is how you solve this

you have 5^x -5^x-3 = (124) (5^y)
step 1: 5^x (1-5^-3) =(124) (5^y)
Step 2: 5^x(1 - 1/5^3) = (124) (5^y)
Step 3: 5^x(1- 1/125) = (124) (5^y)
Step 4: 5^x (125-1)/125 = (124) (5^y)
Step 5: 5^x (124/125) = (124) (5^y)
Step 6: 5^x =[(124) (5^y) (125) ]/124
Step 7: 5^x = (125) (5^y)
Step 8: 5^x = 5^3 (5^y)
Step 9: x = 3 +y --> y = x -3
for explaining purposes I broke it down in to 9 steps. It should not take you more than 5 steps to solve this in term of y.

Your answer may be right. But it is not good practice to do long steps in GMAT. Time is critical.
_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

Intern
Joined: 30 Nov 2015
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

22 Feb 2016, 11:55
I have a very hard time believing this is a sub 600 level question
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 117

Kudos [?]: 1342 [1] , given: 789

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

22 Feb 2016, 12:06
1
This post received
KUDOS
Expert's post
secterp wrote:
I have a very hard time believing this is a sub 600 level question

The trick with GMAT quant is not the level of questions but the time constraint. For PS, you either adopt the traditional algebraic method that can sometimes very time consuming or you can use the options to your advantage as mentioned below.

Let x=3 as you have a power of 3 and I wanted non negative powers of 5. Let see if we get values of 3 or -3 or 0 or 9 or 12 (based on the 5 options given) for y when we do RHS = LHS from the given equation of 5^x – 5^(x- 3) = 124*5^y.

When x =0, the LHS becomes

5^x-5^(x-3)=5^3-5^0=125-1=124.

RHS = 124*5^y and for LHS=RHS , the only way this is possible is when y=0 , giving you y=x-3 as the correct answer. Thus, C is the correct answer.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Intern
Joined: 23 Sep 2016
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 369

Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

21 Oct 2016, 13:14
Bunuel wrote:
alltimeacheiver wrote:
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

$$5^x-5^{x-3}=124*5^y$$ --> factor out $$5^{x-3}$$: $$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3}=5^y$$ --> bases are equal so we can equate the powers: $$y=x-3$$.

Answer: C.

alltimeacheiver format the questions correctly.

Hi Bunuel

Would factoring it like this be correct?

$$5^x-5^{x-3}=124*5^y$$
$$5^{x}(1-5^{-3})=124*5^y$$ --> x-3 = y
Intern
Joined: 23 Sep 2016
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 369

Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

21 Oct 2016, 13:15
Bunuel wrote:
alltimeacheiver wrote:
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

$$5^x-5^{x-3}=124*5^y$$ --> factor out $$5^{x-3}$$: $$5^{x-3}(5^3-1)=124*5^y$$ --> $$5^{x-3}=5^y$$ --> bases are equal so we can equate the powers: $$y=x-3$$.

Answer: C.

alltimeacheiver format the questions correctly.

Hi Bunuel

Would factoring it like this be correct?

$$5^x-5^{x-3}=124*5^y$$
$$5^{x}(1-5^{-3})=124*5^y$$ --> x-3 = y
Intern
Joined: 20 Jan 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

Show Tags

14 Nov 2016, 06:34
PareshGmat wrote:
$$5^x – 5^{(x- 3)} = 124*5^y$$

Re-write as

$$5^x – 5^{(x- 3)} = (125 - 1 ) * 5^y$$

$$5^x – 5^{(x- 3)} = 125* 5^y - 5^y$$

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

LHS = RHS, so equating the powers

y = x+3 ; Answer = C

Please correct the answer as "x-3"
If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?   [#permalink] 14 Nov 2016, 06:34
Similar topics Replies Last post
Similar
Topics:
1 If x = y+3+4.5x and y = x+18, what is the value of x/y ? 2 14 Jul 2016, 00:45
1 X is a prime number bigger than 10. Also, Y = X+X^3+X^5+X^7. What is 2 07 Jun 2016, 06:35
2 Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 4 09 Dec 2015, 07:41
6 If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 4 29 Nov 2014, 18:10
4 If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 15 24 Aug 2012, 04:04
Display posts from previous: Sort by

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

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

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.