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What is the value of t ?

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What is the value of t ?  [#permalink]

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New post Updated on: 02 Oct 2013, 01:06
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What is the value of t ?

(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) \(\sqrt{t^4} = 16\)

Originally posted by jlgdr on 01 Oct 2013, 14:28.
Last edited by Bunuel on 02 Oct 2013, 01:06, edited 1 time in total.
Edited the second statement.
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Re: What is the value of t ?  [#permalink]

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New post Updated on: 02 Oct 2013, 09:03
jlgdr wrote:
What is the value of t ?

(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) t^1/4 = 16

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:
http://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:
http://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:
http://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 :-)
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Originally posted by mikemcgarry on 01 Oct 2013, 15:28.
Last edited by mikemcgarry on 02 Oct 2013, 09:03, edited 2 times in total.
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Re: What is the value of t ?  [#permalink]

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New post 01 Oct 2013, 15:33
jlgdr wrote:
What is the value of t ?
(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) t^1/4 = 16

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.

Was this your question?
Mike :-)
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Re: What is the value of t ?  [#permalink]

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New post 01 Oct 2013, 15:55
mikemcgarry wrote:
jlgdr wrote:
What is the value of t ?

(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) t^1/4 = 16

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:
http://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:
http://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:
http://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 :-)


t^2 + 8t + 16 = 0
Shouldn't this be: (t + 4)^2 = 0 ?
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Re: What is the value of t ?  [#permalink]

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New post 01 Oct 2013, 16:04
igotthis wrote:
t^2 + 8t + 16 = 0
Shouldn't this be: (t + 4)^2 = 0 ?

YES! Absolutely! I just corrected it in my post above.
Thanks,
Mike :-)
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Re: What is the value of t ?  [#permalink]

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New post 01 Oct 2013, 17:13
mikemcgarry wrote:
igotthis wrote:
t^2 + 8t + 16 = 0
Shouldn't this be: (t + 4)^2 = 0 ?

YES! Absolutely! I just corrected it in my post above.
Thanks,
Mike :-)


Sorry, I know this statement is suff. since it gives a unique value...but shouldn't t = -4 then?
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Re: What is the value of t ?  [#permalink]

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New post 02 Oct 2013, 01:09
1
jlgdr wrote:
What is the value of t ?

(1) The average (arithmetic mean) of t^2 and 8t is –8.
(2) \(\sqrt{t^4} = 16\)


NOTE: edited the second statement.

What is the value of t ?

(1) The average (arithmetic mean) of t^2 and 8t is –8 --> t^2 + 8t = -8*2 --> t^2 + 8t + 16 = 0 --> (t+4)^2 = 0 --> t = -4. Sufficient.

(2) \(\sqrt{t^4} = 16\) --> t^2 = 16 --> t = -4 or t = 4. Not sufficient.

Answer: A.

Hope it helps.
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Re: What is the value of t ?  [#permalink]

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New post 02 Oct 2013, 09:04
igotthis wrote:
Sorry, I know this statement is suff. since it gives a unique value...but shouldn't t = -4 then?

Yes, just changed it.
Mike :-)
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Re: What is the value of t ?  [#permalink]

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