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

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  11 Feb 2011, 02:17
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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.
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Re: ps [#permalink]  11 Feb 2011, 04:13
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Expert's post
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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.
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Re: ps [#permalink]  18 Feb 2011, 11:17
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u can also plug in x=3. makes it very simple.
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Re: ps [#permalink]  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

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?
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Kudos [?]: 57420 [0], given: 8811

Re: ps [#permalink]  20 Sep 2012, 13:14
Expert's post
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?

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

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.
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  12 Dec 2012, 18:52
1
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$${5^{x}}\frac{124}{125}=124(5^y)$$
$$5^{x}=5^{y+3}$$
$$x=y+3-->y=x-3$$

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  13 Dec 2012, 02:25
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Expert's post
2
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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)
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 24 Jan 2012 Posts: 10 Followers: 0 Kudos [?]: 80 [0], given: 3 Re: ps [#permalink] 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: 1854 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 27 Kudos [?]: 1226 [1] , given: 193 If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] 26 Feb 2014, 19:47 1 This post received KUDOS $$5^x – 5^{(x- 3)} = 124*5^y$$ 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: 7304 Followers: 384 Kudos [?]: 93 [0], given: 0 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] 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: 761 Followers: 12 Kudos [?]: 138 [0], given: 3 Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] 29 Mar 2015, 07:10 Expert's post 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
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  07 Aug 2015, 16:29
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.
If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?   [#permalink] 07 Aug 2015, 16:29
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