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

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Manager
Joined: 23 Dec 2013
Posts: 152
Location: United States (CA)
GMAT 1: 710 Q45 V41
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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16 Jul 2017, 10:33
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

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

5^(x-3)*(5^3 - 1) = 124*5^y

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

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

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16 Oct 2017, 21:03
5^x−5^(x−3)=124∗5^y
5^x−5^(x−3)=(125-1)∗5^y
5^x−5^(x−3)=(5^3-1)*5^y
5^x−5^(x−3)=5^(3+y)-5^y
x=3+y or x-3=y

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

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21 Jan 2018, 04:41
Would you not say this is a 700 question?

Also, the source is Gmat Prep Extension Pack 1 (at least I have found this question here).

Thanks,
Fernando
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Joined: 30 Jan 2018
Posts: 2
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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11 Mar 2018, 09:19
VeritasPrepKarishma wrote:
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

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)

So what is the mistake in this method:

5^x - 5^(x - 3) = (5^3 - 5^0) * 5^y
5^x - 5^(x - 3) = (5^3 - 1) * 5^y
5^x - 5^(x - 3) = 5^3y - 5^y

3y = x AND y = x-3 - this is enough for correct answer
x = y+3
y + 3 = 3y
y = 1.5
x =4.5

Clearly, something is off with the above, but I have no idea what!
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Joined: 22 May 2016
Posts: 2204
If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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13 Mar 2018, 18:06
Manychips wrote:
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

So what is the mistake in this method:

5^x - 5^(x - 3) = (5^3 - 5^0) * 5^y
5^x - 5^(x - 3) = (5^3 - 1) * 5^y
5^x - 5^(x - 3) = 5^3y - 5^y

3y = x AND y = x-3 - this is enough for correct answer
x = y+3
y + 3 = 3y
y = 1.5
x =4.5

Clearly, something is off with the above, but I have no idea what!

Manychips , the highlighted part should be:
(3 + y) or (y + 3).
$$5^3*5^{y}=5^{(3+y)}$$

You multiplied the exponents.

Easy mistake.
Hope that helps.
CEO
Joined: 11 Sep 2015
Posts: 3235
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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19 Apr 2018, 12:11
Top Contributor
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

One option is to rewrite the left side of the equation by factoring out 5^(x-3)
So, we get: 5^(x-3)[5^3 - 1] = (124)(5^y)
Evaluate to get: 5^(x-3)[125 - 1] = (124)(5^y)
Simplify to get: 5^(x-3)[124] = (124)(5^y)
Divide both sides by 124 to get: 5^(x-3) = 5^y
So, x-3 = y

-----------------------------------------------------
ASIDE: A lot of students struggle to see how we can factor 5^x - 5^(x-3) to get 5^(x-3)[5^3 - 1]
Sure, they may be okay with straightforward factoring like these examples:
k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)
But they have problems when the exponents are variables.

IMPORTANT: Notice that, each time, the greatest common factor of both terms is the term with the smaller exponent.

So, in the expression 5^x - 5^(x-3), the term with the smaller exponent is 5^(x-3, so we can factor out 5^(x-3)

Likewise, w^x + x^(x+5) = w^x(1 + w^5)
And 2^x - 2^(x-2) = 2^(x-2)[2^2 - 1]
------------------------------------------------------------

Cheers,
Brent
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Joined: 11 Sep 2015
Posts: 3235
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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19 Apr 2018, 12:12
Top Contributor
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

Another option is to PLUG IN a value for x and see what kind of relationship we get between x and y.
There are two "nice" x-values to plug in. They are x = 0 and x = 3, since we can easily use these to evaluate 5^x and 5^(x-3). Of these two values, x = 3 is the easier one to plug in.
So, let's plug in x = 3
We get: 5^3 - 5^(3-3) = (124)(5^y)
Simplify to get: 125 - 1 = (124)(5^y)
Simplify to get: 124 = (124)(5^y)
Divide both sides by 124 to get: 1 = 5^y
Solve for y to get: y = 0

So, when x = 3, y = 0.

Now we'll check the answer choices to see which one satisfies this relationship.
A) y = x... So, we get 0 = 3 (NOPE)
B) y = x - 6... So, we get 0 = 3 - 6 (NOPE)
C) y = x - 3... So, we get 0 = 3 - 3 IT WORKS!
D) y = 2x + 3... So, we get 0 = 2(3) + 3 (NOPE)
E) y = 2x + 6... So, we get 0 = 2(3) + 6 (NOPE)

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

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03 Oct 2018, 12:02
Hi,

I don't understand how all yall are factoring 5^x-3 out of 5^x-5^x-3 - isn't the only common factor 5^x???? I am getting 5^x(1-5^-3) for the left side of the equation
Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? &nbs [#permalink] 03 Oct 2018, 12:02

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