## powers and roots

##### This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 27
Joined: 28 Jan 2012
Followed by:1 members

### powers and roots

by klaud » Sun Feb 12, 2012 3:35 pm
Question 1

All of the following are equal except:

A)2^20
B)2^19+2^19
C)4^10
D)4^5+4^5
E)16^5

Question 2

2âˆš3+3âˆš2
-------- =
âˆš2

A)2+2âˆš3
B)2+âˆš6
C)2+3âˆš6
D)3+2âˆš3
E)3+âˆš6

Senior | Next Rank: 100 Posts
Posts: 61
Joined: 13 Mar 2011
Thanked: 1 times
by luiscarlos59 » Sun Feb 12, 2012 3:40 pm

Q2=E , use the reciprocal to cancel out 2 sqrt 3 / sqrt 2 which equals sqrt 6. And 3sqrt2 / sqrt 2 cancels out to 3. So 3 + sqrt 6

Legendary Member
Posts: 1085
Joined: 15 Apr 2011
Thanked: 158 times
Followed by:21 members
by pemdas » Sun Feb 12, 2012 4:05 pm
algebraic simplification is required.
B) 2^19+2^19=2*(2^19)=2^(19+1)=2^20, this isn't correct answer.

the correct choice is d

4^5+4^5=2*4^5=2*2^10=2^(10+1)=2^11
Success doesn't come overnight!

### GMAT/MBA Expert

GMAT Instructor
Posts: 3835
Joined: 02 Apr 2010
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770
by Anurag@Gurome » Sun Feb 12, 2012 8:01 pm
klaud wrote:Question 1

All of the following are equal except:

A)2^20
B)2^19+2^19
C)4^10
D)4^5+4^5
E)16^5
A)2^20
B)2^19 + 2^19 = 2^19(1 + 1) = 2^19 * 2 = 2^20
C)4^10 = 2^20
D)4^5+4^5 = 2^10 + 2^10 = 2^10(1 + 1) = 2^11
E)16^5 = (2^4)^5 = 2^20

Only [spoiler](D)[/spoiler] is not equal to other answer choices.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

GMAT with Gurome

### GMAT/MBA Expert

GMAT Instructor
Posts: 3835
Joined: 02 Apr 2010
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770
by Anurag@Gurome » Sun Feb 12, 2012 8:08 pm
Question 2

2âˆš3+3âˆš2
-------- =
âˆš2

A)2+2âˆš3
B)2+âˆš6
C)2+3âˆš6
D)3+2âˆš3
E)3+âˆš6
Multiply the numerator and denominator of given fraction by âˆš2,
(2âˆš3 + 3âˆš2)/âˆš2 = âˆš2(2âˆš3 + 3âˆš2)/(âˆš2)(âˆš2) = [2âˆš6 + 3(âˆš2)(âˆš2)]/2 = [2âˆš6 + 6]/2 = âˆš6 + 3

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)