Exponent Problem
This topic has expert replies
- theboyleman32
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Mon Apr 07, 2014 12:27 pm
- Followed by:1 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
One option is to rewrite the left side of the equation by factoring out 5^(x-3)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
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
Answer: C
-------------------------------
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
- kvcpk
- Legendary Member
- Posts: 1893
- Joined: Sun May 30, 2010 11:48 pm
- Thanked: 215 times
- Followed by:7 members
5^x - 5^(x-3) = 124 * (5^y)theboyleman32 wrote:assistance with this problem would be greatly appreciated!!!
5^x - 5^x/5^3 = 124 * (5^y)
Taking 5^x common,
5^x(1-(1/125)) = 124 * (5^y)
5^x(124/125) = 124 * (5^y)
Canceling out 124 on both sides
5^x/125 = 5^y
5^(x-3) = 5^y
Hence y=x-3
Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Another option is to PLUG IN a value for x and see what kind of relationship we get between x and y.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
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)
Answer: C
Cheers,
Brent
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Plug in a value for x and solve for y.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
Let x=3.
Then:
5³ - 5� = (124)(5^y)
124 = (124)(5^y)
1 = 5^y
y=0. This is our target.
Now plug x=3 into the answers to see which yield our target value of 0.
Only C works:
x-3 = 3-3 = 0.
The correct answer is C.
Last edited by GMATGuruNY on Wed Dec 17, 2014 2:46 pm, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here are two more practice questions where we have variable exponents:
https://www.beatthegmat.com/is-5-k-less- ... 74188.html
https://www.beatthegmat.com/question-on- ... 68718.html
Cheers,
Brent
https://www.beatthegmat.com/is-5-k-less- ... 74188.html
https://www.beatthegmat.com/question-on- ... 68718.html
Cheers,
Brent