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# What is the value of t ?

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Joined: 06 Sep 2013
Posts: 1521
Concentration: Finance
What is the value of t ?  [#permalink]

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Updated on: 02 Oct 2013, 02:06
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71% (01:16) correct 29% (01:24) wrong based on 159 sessions

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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, 15:28.
Last edited by Bunuel on 02 Oct 2013, 02:06, edited 1 time in total.
Edited the second statement.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

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Updated on: 02 Oct 2013, 10:03
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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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

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01 Oct 2013, 16:33
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.

Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 10 Sep 2013
Posts: 69
Concentration: Sustainability, International Business
Re: What is the value of t ?  [#permalink]

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01 Oct 2013, 16:55
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 ?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

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01 Oct 2013, 17:04
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
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 10 Sep 2013
Posts: 69
Concentration: Sustainability, International Business
Re: What is the value of t ?  [#permalink]

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01 Oct 2013, 18:13
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?
Math Expert
Joined: 02 Sep 2009
Posts: 60644
Re: What is the value of t ?  [#permalink]

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02 Oct 2013, 02:09
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.

Hope it helps.
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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

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02 Oct 2013, 10:04
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
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Re: What is the value of t ?  [#permalink]

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Re: What is the value of t ?   [#permalink] 15 Aug 2018, 07:15
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