Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61190

If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
23 Sep 2015, 21:35
Question Stats:
79% (01:36) correct 21% (01:54) wrong based on 204 sessions
HideShow timer Statistics
If \(5^x  5^{x1}= 500\), what is the value of (x  1)^2? (A) 1 (B) 4 (C) 9 (D) 25 (E) 36 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Senior Manager
Joined: 05 Apr 2015
Posts: 353

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
23 Sep 2015, 22:55
5^x  (5^x/5) = 500
=> 5^x(11/5) = 500
=> 5^x * (4/5) = 500
=> 5^(x1) = 125
=> x=4
hence (41)^2 = 9 hence C.
Regards, Dom.



Intern
Joined: 27 Apr 2015
Posts: 32
Location: India
WE: Operations (Telecommunications)

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 00:45
5^x  5^(x1) = 500 => 5^(x1) {5  1} =500 => 5^(x1) 4 = 500 => 5^(x1) 2^2 = 5^3 2^2 => 5^(x1) = 5^3 => x1 = 3 => (x1)^2 = 3^2 = 9
Answer: C



Intern
Joined: 28 May 2015
Posts: 8
Concentration: Finance, Economics
GPA: 4

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 01:28
Can you not just work this out?
5^4  5^(41) = 625  125 = 500
Therefore x is 4 so (x1)^2 = (41)^2 = 9 (c)
This way just seems quicker to me!



Manager
Joined: 29 Jul 2015
Posts: 150

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 05:06
Bunuel wrote: If \(5^x  5^{x1}= 500\), what is the value of (x  1)^2?
(A) 1 (B) 4 (C) 9 (D) 25 (E) 36
Kudos for a correct solution. \(5^x  5^{x1}= 500\) 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 \(5^{x1}\) = 125 or \(5^{x1}= 5^3\) or \(x1 = 3\) or \((x1)^2 = 9\) Answer: C



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4318
Location: Canada

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 06:10
DavidSt wrote: Can you not just work this out?
5^4  5^(41) = 625  125 = 500
Therefore x is 4 so (x1)^2 = (41)^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
_________________
Test confidently with gmatprepnow.com



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4318
Location: Canada

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 06:18
Bunuel wrote: If \(5^x  5^{x1}= 500\), 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 \(5^x  5^{x1}= 500\) to get \(5^2  5^{21}= 500\) 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 \(5^x  5^{x1}= 500\) to get \(5^3  5^{31}= 500\) 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 \(5^x  5^{x1}= 500\) to get \(5^4  5^{41}= 500\) Simplify: 625  125 = 500 WORKS! Answer: C Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Manager
Joined: 22 Aug 2012
Posts: 73
Concentration: Technology

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 09:09
I believe the answer is C. Please see below for explanation
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
Answer C



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16104
Location: United States (CA)

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 10:40
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^(X1), 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^(41) = 5^4  5^3 = 625  125 = 500 Since we now know the value of X, we can answer the question  the value of (X1)^2 = (41)^2 = 9 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 19 Dec 2014
Posts: 35

If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 12:22
\(5^x−5^{x1}\)=500
This can be simplified to
\(5^x\) * (4/5) =\(5^3\) * \(2^2\)
\(5^{x1}\) * \(2^2\) = \(5^3\) * \(2^2\)
x  1 = 3
\((x1) ^ 2\) = 9
Answer = C



Intern
Joined: 28 May 2015
Posts: 8
Concentration: Finance, Economics
GPA: 4

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
24 Sep 2015, 17:28
GMATPrepNow wrote: DavidSt wrote: Can you not just work this out?
5^4  5^(41) = 625  125 = 500
Therefore x is 4 so (x1)^2 = (41)^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 68 (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 625125 = 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
Joined: 31 May 2014
Posts: 5
Location: India
Concentration: Technology, Strategy
Schools: Stern '21, Kelley '21 (D), McCombs '21, Tepper '21, Marshall '21 (D), LBS '21, Georgia Tech '21, Rotman '21 (S), Jones '21 (D), Foster '21 (WD), Arizona State'21, GWU '21
GPA: 3.2

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
25 Sep 2015, 22:12
Bunuel wrote: If \(5^x  5^{x1}= 500\), 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 \(5^x  5^{x1}= 500\) L.H.S R.H.S \(5^{x1}(51)\) = \(5^3 * 2^2\) \(5^{x1}(4)\) = \(5^3 * 2^2\) \(5^{x1}(4)\) = \(5^3 * 2^2\) Therefore x1 = 3 Square both sides \((x1)^2\) = 9 Cheers



Intern
Joined: 04 Jun 2008
Posts: 6

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
26 Sep 2015, 23:27
(5^x)  (5^x)*5 = 500 5^x (15) = 500 5^x = 125 5^x = 5^3 x=3 => (31)^2 = 4



NonHuman User
Joined: 09 Sep 2013
Posts: 14072

Re: If 5^x  5^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
Show Tags
06 Jan 2020, 04:21
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^{x1}= 500 , what is the value of (x  1)^2?
[#permalink]
06 Jan 2020, 04:21






