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jlgdr
Joined: 06 Sep 2013
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Schools: Wharton '17 (A) HBS '17 (WA$)
A
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What is the value of t ?
(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) \(\sqrt{t^4} = 16\)
(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) \(\sqrt{t^4} = 16\)
Updated on: 02 Oct 2013, 10:03
Originally posted by mikemcgarry on 01 Oct 2013, 16:28.
Last edited by mikemcgarry on 02 Oct 2013, 10:03, edited 2 times in total.
Last edited by mikemcgarry on 02 Oct 2013, 10:03, edited 2 times in total.
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jlgdr
I'm happy to help
, but I disagree with the OA given. Statement #1: The average (arithmetic mean) of t^2 and 8t is –8.
[t^2 + 8t]/2 = –8
t^2 + 8t = –16
t^2 + 8t + 16 = 0
(t + 4)^2 = 0
t = - 4
See:
https://magoosh.com/gmat/2013/three-alge ... -the-gmat/
This statement produces a unique value of t, and thus is sufficient.
Statement #2: t^1/4 = 16
I will assume what this means is t^(1/4) = 16, only because I can't think of another sensible interpretation of the ambiguity. Incidentally, on the issue of this ambiguity, and the underlying mathematical principles, read:
https://magoosh.com/gmat/2013/gmat-quant ... g-symbols/
Raising a number to the power of (1/4) is equivalent to taking the fourth root of a number. We can't take an even root of negative number, so if the fourth root of t equals anything sensible, then t absolutely must be positive. We would raise both sides to the fourth power to get a unique value of t. See:
https://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
(BTW, that value would be t = 2^16 = 65,536, but absolutely no one expects you to get that without a calculator!!)
This statement also produces a unique value of t, and thus is also sufficient.
This would produce an OA of (D). I don't know whether you copied something incorrectly about statement two --- perhaps another phrasing would make that statement insufficient. Also, as this question currently stands, the two statements produce different values for t. This falls short of the standard that the GMAT keeps on DS --- statements in both statements are mathematically consistent.
Let me know if statement #2 says something else.
Mike
01 Oct 2013, 16:33
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jlgdr
I just did a web search, and found this version of statement #2:
Statement #2: sqrt(t^4) = 16
Unlike the version you quoted, this version would indeed be insufficient, because it would allow for both t = +4 and t = -4. Furthermore, the correct answer from statement #1 is one of the possible answers in statement #2, so indeed, the statements here are mathematically consistent with one another.
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Mike
