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
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Algebra Strategies question
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gmattesttaker2
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Phew, that's a lot of nested brackets! In fact, there are a few extras here.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
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
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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
"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
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GMATGuruNY
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Another approach: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
[(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.
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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].
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