GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Jan 2020, 04:13 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the value of t ?

Author Message
TAGS:

### Hide Tags

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

### Show Tags 00:00

Difficulty:

(N/A)

Question Stats: 71% (01:16) correct 29% (01:24) wrong based on 159 sessions

### HideShow timer Statistics

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 G
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

### Show Tags

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 _________________
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 G
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

### Show Tags

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
Re: What is the value of t ?  [#permalink]

### Show Tags

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 G
Joined: 28 Dec 2011
Posts: 4476
Re: What is the value of t ?  [#permalink]

### Show Tags

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
Re: What is the value of t ?  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 60644
Re: What is the value of t ?  [#permalink]

### Show Tags

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

### Show Tags

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)
Non-Human User Joined: 09 Sep 2013
Posts: 14003
Re: What is the value of t ?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the value of t ?   [#permalink] 15 Aug 2018, 07:15
Display posts from previous: Sort by

# What is the value of t ?  