GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Feb 2020, 23:10 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61190
If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 79% (01:36) correct 21% (01:54) wrong based on 204 sessions

### HideShow timer Statistics

If $$5^x - 5^{x-1}= 500$$, what is the value of (x - 1)^2?

(A) 1
(B) 4
(C) 9
(D) 25
(E) 36

Kudos for a correct solution.

_________________
Senior Manager  B
Joined: 05 Apr 2015
Posts: 353
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
5^x - (5^x/5) = 500

=> 5^x(1-1/5) = 500

=> 5^x * (4/5) = 500

=> 5^(x-1) = 125

=> x=4

hence (4-1)^2 = 9 hence C.

Regards,
Dom.
Intern  B
Joined: 27 Apr 2015
Posts: 32
Location: India
GMAT 1: 730 Q50 V40
WE: Operations (Telecommunications)
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
5^x - 5^(x-1) = 500
=> 5^(x-1) {5 - 1} =500
=> 5^(x-1) 4 = 500
=> 5^(x-1) 2^2 = 5^3 2^2
=> 5^(x-1) = 5^3
=> x-1 = 3
=> (x-1)^2 = 3^2 = 9

Intern  Joined: 28 May 2015
Posts: 8
Concentration: Finance, Economics
GPA: 4
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
Can you not just work this out?

5^4 - 5^(4-1) = 625 - 125 = 500

Therefore x is 4 so (x-1)^2 = (4-1)^2 = 9 (c)

This way just seems quicker to me!
Manager  Joined: 29 Jul 2015
Posts: 150
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

2
Bunuel wrote:
If $$5^x - 5^{x-1}= 500$$, what is the value of (x - 1)^2?

(A) 1
(B) 4
(C) 9
(D) 25
(E) 36

Kudos for a correct solution.

$$5^x - 5^{x-1}= 500$$

or $$5^x - \frac{5^x}{5}= 500$$

or $$5^x(1 - \frac{1}{5})= 500$$

or $$5^x( \frac{4}{5})= 125*4$$

or $$5^{x-1}$$ = 125

or $$5^{x-1}= 5^3$$

or $$x-1 = 3$$

or $$(x-1)^2 = 9$$

GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4318
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

DavidSt wrote:
Can you not just work this out?

5^4 - 5^(4-1) = 625 - 125 = 500

Therefore x is 4 so (x-1)^2 = (4-1)^2 = 9 (c)

This way just seems quicker to me!

How did you "work it out"?
If you guess and tested, that's totally fine, except that approach could take a while.

Cheers,
Brent
_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4318
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

2
Bunuel wrote:
If $$5^x - 5^{x-1}= 500$$, what is the value of (x - 1)^2?

(A) 1
(B) 4
(C) 9
(D) 25
(E) 36

Kudos for a correct solution.

Testing the answer choices could also be pretty quick.

A) 1
This means (x - 1)^2 = 1
So, x - 1 = 1, which mean x = 2
Now plug x = 2 into $$5^x - 5^{x-1}= 500$$ to get $$5^2 - 5^{2-1}= 500$$
Simplify: 25 - 5 = 500
Doesn't work

B) 4
This means (x - 1)^2 = 4
So, x - 1 = 2, which mean x = 3
Now plug x = 3 into $$5^x - 5^{x-1}= 500$$ to get $$5^3 - 5^{3-1}= 500$$
Simplify: 125 - 25 = 500
Doesn't work

C) 9
This means (x - 1)^2 = 9
So, x - 1 = 3, which mean x = 4
Now plug x = 4 into $$5^x - 5^{x-1}= 500$$ to get $$5^4 - 5^{4-1}= 500$$
Simplify: 625 - 125 = 500
WORKS!

Cheers,
Brent
_________________
Manager  Joined: 22 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
1

If 5^x−5^x−1=500, what is the value of (x - 1)^2?

5^x(1 - 1/5 ) = 5* 2*5 * 2*5

5^x(4/5) = 5^3 * 2^2

5^x * 4 = 5^4 * 2^2

5^x * 2^2 = 5^4 * 2^2

Which means that x = 4

Replacing x with 4 in (x - 1)^2 gives 9

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16104
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
Hi All,

This question has a great 'brute force' shortcut to it (if you're comfortable doing some basic multiplication).

Since the answer choices are all perfect squares, X MUST be an integer.

We're also given 5^X and 5^(X-1), which are two consecutive "powers" of 5. We're told that subtracting the smaller value from the larger value will give us 500...

Let's start listing powers of 5 until we find two consecutive powers that differ by 500....

5^0 = 1
5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625

STOP. 625 - 125 = 500, so X MUST be 4. To confirm...

5^4 - 5^(4-1) =
5^4 - 5^3 =
625 - 125 = 500

Since we now know the value of X, we can answer the question - the value of (X-1)^2 = (4-1)^2 = 9

GMAT assassins aren't born, they're made,
Rich
_________________
Intern  Joined: 19 Dec 2014
Posts: 35
If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
$$5^x−5^{x-1}$$=500

This can be simplified to

$$5^x$$ * (4/5) =$$5^3$$ * $$2^2$$

$$5^{x-1}$$ * $$2^2$$ = $$5^3$$ * $$2^2$$

x - 1 = 3

$$(x-1) ^ 2$$ = 9

Intern  Joined: 28 May 2015
Posts: 8
Concentration: Finance, Economics
GPA: 4
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

GMATPrepNow wrote:
DavidSt wrote:
Can you not just work this out?

5^4 - 5^(4-1) = 625 - 125 = 500

Therefore x is 4 so (x-1)^2 = (4-1)^2 = 9 (c)

This way just seems quicker to me!

How did you "work it out"?
If you guess and tested, that's totally fine, except that approach could take a while.

Cheers,
Brent

To be honest I have tried to memorize the lowest numbers and their exponents up to around 6-8 (depending on the number i.e. 2^8 but not 5^8) as that was a tip from the Manhattan Guides.

As soon as I saw 5^x I just thought: 5, 25, 125, 625 and instantly noticed that 625-125 = 500.

But I can see the merit in the other way of factoring as the questions may not all have an easy solution like this one!
Intern  B
Joined: 31 May 2014
Posts: 5
Location: India
Concentration: Technology, Strategy
GMAT 1: 700 Q47 V39
GPA: 3.2
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

1
Bunuel wrote:
If $$5^x - 5^{x-1}= 500$$, what is the value of (x - 1)^2?

(A) 1
(B) 4
(C) 9
(D) 25
(E) 36

Kudos for a correct solution.

Simplify both sides to their basic roots

$$5^x - 5^{x-1}= 500$$

L.H.S R.H.S
$$5^{x-1}(5-1)$$ = $$5^3 * 2^2$$
$$5^{x-1}(4)$$ = $$5^3 * 2^2$$
$$5^{x-1}(4)$$ = $$5^3 * 2^2$$

Therefore
x-1 = 3
Square both sides
$$(x-1)^2$$ = 9

Cheers
Intern  Joined: 04 Jun 2008
Posts: 6
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

(5^x) - (5^x)*5 = 500
5^x (1-5) = 500
5^x = -125
5^x = -5^3
x=3 => (3-1)^2 = 4
Non-Human User Joined: 09 Sep 2013
Posts: 14072
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?  [#permalink]

### Show Tags

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.
_________________ Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?   [#permalink] 06 Jan 2020, 04:21
Display posts from previous: Sort by

# If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?   