BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Algebra Strategies question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Algebra Strategies question

by gmattesttaker2 » Sun Feb 03, 2013 12:05 pm
Hello,

I was just wondering if you can please assist here. This question is from MGMAT Strategy Guide2 (P. 125)

(((3/4)^3))^(1/4) > 3/4

True or False

Answer: True


My approach was as follows:

3/4 approximates to 4/4

So, ((1)^3)^(1/4) = 1^(3/4) = 1^1 = 1

So,1 > 1 is False

Can you please assist here? Thanks a lot.


Best Regards,
Sri
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Feb 03, 2013 12:31 pm
gmattesttaker2 wrote:Hello,

I was just wondering if you can please assist here. This question is from MGMAT Strategy Guide2 (P. 125)

(((3/4)^3))^(1/4) > 3/4

True or False

Answer: True
Phew, that's a lot of nested brackets! In fact, there are a few extras here.
Perhaps adding some square brackets will help. We get:
Is [(3/4)^3]^(1/4) > 3/4?

To begin, we can apply the power of a power rule to get:
Is (3/4)^(3/4) > 3/4?

If recognize that 0 < 3/4 < 1, we can see where (3/4)^(3/4) fits in the following pattern:
(3/4)^4 = 81/256
(3/4)^3 = 27/64
(3/4)^2 = 9/16
(3/4)^1 = 3/4
(3/4)^(3/4) = some value between 3/4 and 1
(3/4)^0 = 1
(3/4)^(-1) = 4/3
(3/4)^(-2) = 16/9

This means that (3/4)^(3/4) is greater than 3/4.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Feb 03, 2013 12:34 pm
There's also a "rule" that says,
"If 0<x<1 and y<1, then x^y > x"

So, (3/4)^(3/4) > 3/4

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
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

by GMATGuruNY » Sun Feb 03, 2013 6:02 pm
gmattesttaker2 wrote:Hello,

I was just wondering if you can please assist here. This question is from MGMAT Strategy Guide2 (P. 125)

(((3/4)^3))^(1/4) > 3/4 ?

True or False
Another approach:

[(3/4)³]¹´� > (3/4) ?

To clear the fractional exponent, raise each side to the fourth power:
(3/4)³ > (3/4)�

Distribute the exponents:
3³/4³ > 3�/4�

Cross-multiply:
3³4� > 3�4³

Divide each side by 3³4³:
4 > 3.

Thus, it is TRUE that the lefthand side is greater than the righthand side.
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
Top
Post new topic Post Reply
• Page 1 of 1