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Temp Avg

by preciousrain7 » Tue Jan 15, 2008 4:54 pm
If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 4x
(C) (5/3)x
(D) (3/2)x
(E) (3/5)x

I cannot for the life of me figure out why the official ans is:

official ans is B
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by desihokie » Tue Jan 15, 2008 6:03 pm
is the answer B? If yes, i could try to explain.
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by preciousrain7 » Tue Jan 15, 2008 6:24 pm
desihokie wrote:is the answer B? If yes, i could try to explain.
yes! plz do explain
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by sibbineni » Tue Jan 15, 2008 6:26 pm
Answer is B

let us consider 5 numbers as 1,2,3,4,5

and then the AM is calculated by

1+2+3+4+5/5=x

x=3

To find the sum of the 3 greatest numbers

3+4+5=12

3*4=4x (since x=3)


Suggest me i am Wrong
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by preciousrain7 » Tue Jan 15, 2008 6:33 pm
sibbineni wrote:Answer is B

let us consider 5 numbers as 1,2,3,4,5

and then the AM is calculated by

1+2+3+4+5/5=x

x=3

To find the sum of the 3 greatest numbers

3+4+5=12

3*4=4x (since x=3)


Suggest me i am Wrong

Thanks! I was picked numbers like 4+5+6+10+15. The answer doesn't hold true when I use those numbers :cry:
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by desihokie » Tue Jan 15, 2008 6:58 pm
I did the same thing, i tool 10.20.30.40 and 50 as my number and 4X made sense.

preciousrain7, even with your pics, the sum of 3 greates numbers is 31 which is very close to 4 times average of 8

May be there is a better more definite way of solving this problem, anyone?
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Re: Temp Avg

by Stuart@KaplanGMAT » Tue Jan 15, 2008 7:21 pm
preciousrain7 wrote:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 4x
(C) (5/3)x
(D) (3/2)x
(E) (3/5)x
We know that the biggest number is a set must be greater than the average of the set. Therefore, eliminate answer (e).

We also know that the sum of the set = # of terms * average. For a 5 term set, that means that the sum of the WHOLE set = 5x. Eliminate answer (a).

Finally, we know that the biggest 3 numbers in a set have to be greater than 3/5 of the sum of the entire set (otherwise they wouldn't be the 3 biggest numbers). So, we know that:

Sum(3 biggest) > 3/5 (5x)
Sum(3 biggest) > 3x

Therefore, we get the inequality 3x < sum(3biggest) < 5x

The only answer that fits in this range is (b)
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by simplyjat » Tue Jan 15, 2008 8:52 pm
The question is absurd, It asks for a range without specifying the domain.
All the answers that I am seeing are assuming that temperature can only be positive.

What if temperature is negative! Negative temperatures are not unusual on Fahrenheit and Celsius scale; they are impossible on Kelvin scale though.

When we take negative temperatures as possible, almost all answers are correct ! Simply ignore the question and don't trust the source
simplyjat
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by Stuart@KaplanGMAT » Tue Jan 15, 2008 9:13 pm
simplyjat wrote:The question is absurd, It asks for a range without specifying the domain.
All the answers that I am seeing are assuming that temperature can only be positive.

What if temperature is negative! Negative temperatures are not unusual on Fahrenheit and Celsius scale; they are impossible on Kelvin scale though.

When we take negative temperatures as possible, almost all answers are correct ! Simply ignore the question and don't trust the source
How about reading the question more carefully!
If the average (arithmetic mean) of 5 positive temperatures is x degrees
:o
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by simplyjat » Tue Jan 15, 2008 9:54 pm
Sorry I missed the question :(
Ignore my last post
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Re: Temp Avg

by preciousrain7 » Wed Jan 16, 2008 12:28 pm
Stuart Kovinsky wrote:
preciousrain7 wrote:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 4x
(C) (5/3)x
(D) (3/2)x
(E) (3/5)x
We know that the biggest number is a set must be greater than the average of the set. Therefore, eliminate answer (e).

We also know that the sum of the set = # of terms * average. For a 5 term set, that means that the sum of the WHOLE set = 5x. Eliminate answer (a).

Finally, we know that the biggest 3 numbers in a set have to be greater than 3/5 of the sum of the entire set (otherwise they wouldn't be the 3 biggest numbers). So, we know that:

Sum(3 biggest) > 3/5 (5x)
Sum(3 biggest) > 3x

Therefore, we get the inequality 3x < sum(3biggest) < 5x

The only answer that fits in this range is (b)
Thanks a lot Stuart.
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by kaplansteve » Wed Jan 16, 2008 1:35 pm
This might have been said, but picking numbers didn't work because it won't always get you to 4x. It's not asking for a definitive answer, just a POSSIBLE answer. 4x is just one of many possible answers.

Cheers,
Steve
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by preciousrain7 » Wed Jan 16, 2008 5:00 pm
kaplansteve wrote:This might have been said, but picking numbers didn't work because it won't always get you to 4x. It's not asking for a definitive answer, just a POSSIBLE answer. 4x is just one of many possible answers.

Cheers,
Steve
very good point!
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