It is currently 21 Oct 2017, 16:26

### 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 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: 12

Kudos [?]: 120 [6], given: 1

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

### Show Tags

11 Feb 2011, 03:17
6
KUDOS
43
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:04) correct 21% (01:16) wrong based on 593 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 21 Oct 2017, 09:35, edited 2 times in total.
Renamed the topic and edited the question.

Kudos [?]: 120 [6], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17381 [11], given: 232

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

### Show Tags

13 Dec 2012, 03:25
11
KUDOS
Expert's post
9
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 Kudos [?]: 17381 [11], given: 232 Math Expert Joined: 02 Sep 2009 Posts: 41892 Kudos [?]: 129166 [10], given: 12194 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 11 Feb 2011, 05:13 10 This post received KUDOS Expert's post 11 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. _________________ Kudos [?]: 129166 [10], given: 12194 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1853 Kudos [?]: 2628 [5], given: 193 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 26 Feb 2014, 20:47 5 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 Kudos [?]: 2628 [5], given: 193 Senior Manager Joined: 08 Nov 2010 Posts: 394 Kudos [?]: 128 [4], given: 161 WE 1: Business Development Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 18 Feb 2011, 12:17 4 This post received KUDOS 1 This post was BOOKMARKED u can also plug in x=3. makes it very simple. _________________ Kudos [?]: 128 [4], given: 161 Intern Joined: 21 Feb 2015 Posts: 27 Kudos [?]: 8 [3], given: 23 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 07 Aug 2015, 17:29 3 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. Kudos [?]: 8 [3], given: 23 Senior Manager Joined: 13 Aug 2012 Posts: 458 Kudos [?]: 541 [2], given: 11 Concentration: Marketing, Finance GPA: 3.23 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 12 Dec 2012, 19:52 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. Kudos [?]: 541 [2], given: 11 Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1905 Kudos [?]: 524 [1], given: 23 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] ### Show Tags 29 Mar 2015, 08:10 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

Kudos [?]: 524 [1], given: 23

Intern
Joined: 30 Nov 2015
Posts: 9

Kudos [?]: 4 [1], 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, 12:55
1
KUDOS
I have a very hard time believing this is a sub 600 level question

Kudos [?]: 4 [1], given: 1

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1728 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

### Show Tags

22 Feb 2016, 13:06
1
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
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

Kudos [?]: 1728 [1], given: 792

Intern
Joined: 12 Dec 2011
Posts: 9

Kudos [?]: 24 [0], given: 5

Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE: Management Consulting (Consulting)
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

### Show Tags

20 Sep 2012, 14:05
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

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: $$y=x-3$$.

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

Kudos [?]: 24 [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129166 [0], given: 12194

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

### Show Tags

20 Sep 2012, 14:14
Expert's post
3
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

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: $$y=x-3$$.

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.
_________________

Kudos [?]: 129166 [0], given: 12194

Ryerson (Ted Rogers) Thread Master
Joined: 27 Sep 2015
Posts: 60

Kudos [?]: 62 [0], given: 26

GMAT 1: 410 Q33 V13
WE: Management Consulting (Computer Software)
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

### Show Tags

19 Dec 2015, 13:57
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.

Kudos [?]: 62 [0], given: 26

Intern
Joined: 23 Sep 2016
Posts: 7

Kudos [?]: [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, 14:15
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

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: $$y=x-3$$.

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

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

Manager
Joined: 20 Jan 2017
Posts: 63

Kudos [?]: 7 [0], given: 15

Location: United States (NY)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

### Show Tags

20 Feb 2017, 04:41
Here is how I did it:
1) 124=5^3-1; 5^x-5^x-3=(5^3-1)*5^y; 5^x-5^x-3=5^3y-5^y
2) x=3y; x-3=y

The correct answer is C.

Kudos [?]: 7 [0], given: 15

Manager
Joined: 13 Dec 2013
Posts: 172

Kudos [?]: 26 [0], given: 122

Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

### Show Tags

23 Mar 2017, 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

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: $$y=x-3$$.

alltimeacheiver format the questions correctly.

Factorizing this way also works but do you have any advice for performing factorizations in the simplest way possible. Why or how did you know to factor out 5^(x-3) and not 5^x? Should you take factor out the most complicated term?

5^x – 5^(x- 3) = 124*5^y
5^x(1 - 5^-3) = 124*5^y
5^x(1 - 1/125) = 124*5^y
5^x(124/125) = 124*5^y
Diving through by 124: (5^x)*(1/125) = 5^y
(5^x)*(5^-3) = 5^y
5^(x-3) = 5^y
x-3=y

Kudos [?]: 26 [0], given: 122

SVP
Joined: 08 Jul 2010
Posts: 1836

Kudos [?]: 2280 [0], given: 51

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

### Show Tags

15 May 2017, 21:31
peterpark 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

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

i.e. $$5^{x-3}(5^3 - 1) = (124)(5^y)$$

i.e. $$5^{x-3}(124) = (124)(5^y)$$

i.e. $$5^{x-3} = (5^y)$$

i.e. y = x-3

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2280 [0], given: 51

Senior Manager
Joined: 22 Aug 2013
Posts: 443

Kudos [?]: 131 [0], given: 260

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

### Show Tags

15 May 2017, 22:52
5^(x-3) can be written as 5^x / 5^3. So 5^x - 5^x/5^3 = 5^x (1 - 1/5^3)

or 5^x (1 - 1/125) or 5^x (124/125)

or 124 (5^x/5^3) or 124 [5^(x-3)]

Compare with right hand side of the given equation, y must be = (x-3)

Hence C

Kudos [?]: 131 [0], given: 260

Manager
Joined: 28 May 2014
Posts: 211

Kudos [?]: 134 [0], given: 70

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

### Show Tags

16 May 2017, 10:49
5^x - 5^x-3
= 5^x[1 - 5^(-3)]
= 5^x[1 - 1/(5^3)]
= 5^x[1 - 5^(-3)]
= 5^x[1 - 1/125]
= 5^x*124/125
= 5^x*124/5^(-3)
= 5^(x-3)*124

Again,
(124)(5^y) = 5^(x-3)*124

Hence, y = x-3.

Kudos [?]: 134 [0], given: 70

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1648

Kudos [?]: 848 [0], given: 3

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

### Show Tags

19 May 2017, 06:21
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

We can simplify the given equation:

5^x – 5^(x- 3) = 124*5^y

5^x – (5^x)(5^- 3) = 124*5^y

5^x(1 – (5^- 3)) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(124/125) = 124*5^y

5^x = 124*5^y*(125/124)

5^x = 5^y(125)

5^x = 5^y(5^3)

5^x = 5^y+3

x = y + 3

x - 3 = y

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 848 [0], given: 3

Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?   [#permalink] 19 May 2017, 06:21

Go to page    1   2    Next  [ 22 posts ]

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 | Emoji artwork provided by EmojiOne 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®.