Difficulty level: 700ish
Answer: EIf 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) =
A) 1/25
B) 1/5
C) 5
D) 25
E) 125
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
700-level exponent question
This topic has expert replies
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's a question I just made up.
Difficulty level: 700ish
Difficulty level: 700ish
Brent Hanneson - Creator of GMATPrepNow.com
-
DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
If 2^m = 5 and 5^(1/n) = 3, we can substitute 2^m in place of 5 in the second equation to get 2^m^(1/n) = 3. Raise both sides to the n to getBrent@GMATPrepNow wrote:Here's a question I just made up.
Difficulty level: 700ish
Answer: EIf 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) =
A) 1/25
B) 1/5
C) 5
D) 25
E) 125
2^m = 3^n.
We're looking for (3^n)/2^(-2m), so substitute 2^m in place of 3^n, to get 2^m/2^(-2m) = 2^3m, or (2^m)^3. If 2^m = 5, then (2^m)^3 = 5^3 = 125. Answer is E
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 approach:Brent@GMATPrepNow wrote:If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) =
A) 1/25
B) 1/5
C) 5
D) 25
E) 125
Given: 2^m= 5
We need to determine the value of 2^(-2m)
So, take 2^m= 5 and raise both sides to the power of -2
We get: (2^m)^(-2) = 5^(-2)
Apply Power of a Power rule to get: 2^(-2m) = 5^(-2)
Given: 5^(1/n) = 3
We need to determine the value of 3^n
So, take 5^(1/n) = 3 and raise both sides to the power of n
We get: [5^(1/n)]^n = 3^n
Apply Power of a Power rule to get: 5^1 = 3^n
So, (3^n)/2^(-2m) = (5^1)/[(5^(-2)]
= 5^3
= 125
Answer: E
Brent Hanneson - Creator of GMATPrepNow.com
-
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
An alternate approach is to BALLPARK.Brent@GMATPrepNow wrote:Here's a question I just made up.
Difficulty level: 700ish
If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) =
A) 1/25
B) 1/5
C) 5
D) 25
E) 125
Since the answer choices are very spread out, we can approximate with integer values.
Since 2² = 4, 2^m = 5 implies that m ≈ 2.
Since √5 ≈ 2.24, 5^(1/n) = 3 implies that n ≈ 2.
Thus:
(3^n)/2^(-2m) ≈ (3²)/2¯� = (9)(16) = 144.
Only E is viable.
The correct answer is E.
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
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Recognizing the relationship between what you want and what you're given is crucial here.
We want 3� and 2�²�. We can get the first by raising 5⅟� to the n, and the second by raising 2� to the -2. Then we're set!
We want 3� and 2�²�. We can get the first by raising 5⅟� to the n, and the second by raising 2� to the -2. Then we're set!
