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Easy Average problem or is it?

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by faraz_jeddah » Thu Sep 19, 2013 11:34 pm
If the terms of a sequence t1, t2, ....tn, what is the value of n?
1. The sum of the n terms is 3,124.
2. The average (arithmetic mean) of the n terms is 4.

I was going through this problem and the obvious answer looks like C.

But I wanted to check if I were to replicate this problem on a smaller scale.

What if the problem were restated as

1. the sum of the terms is 9
2. The average is 3

In this case
I could say the series is 0,1,8 where sum is 9 and average is 3. ==> n = 3

I could also say the series is 1,2,3,3 where sum is 9 and average is 3 but n = 4.

My question is what is the impact of the word "series" in the question?
Am I overthinking this simple problem?
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by vinay1983 » Thu Sep 19, 2013 11:48 pm
faraz_jeddah wrote:If the terms of a sequence t1, t2, ....tn, what is the value of n?
1. The sum of the n terms is 3,124.
2. The average (arithmetic mean) of the n terms is 4.

I was going through this problem and the obvious answer looks like C.

But I wanted to check if I were to replicate this problem on a smaller scale.

What if the problem were restated as

1. the sum of the terms is 9
2. The average is 3

In this case
I could say the series is 0,1,8 where sum is 9 and average is 3. ==> n = 3

I could also say the series is 1,2,3,3 where sum is 9 and average is NOT 3 BUT 9/4 2.25 but n = 4.

My question is what is the impact of the word "series" in the question?
Am I overthinking this simple problem?
Good to see you back. I changed the average from 3 to 2.25. Happens:)

Series gives us a concrete idea about the numbers we should consider. Like in the above question you have posted, if it would have been" terms, which are positive and in series (such as A.P or G.P) would gives us definite numbers to work with.Also I feel the no. of numbers is restricted by the average. In this case to get 3 as average we should have N numbers such that we get a integer as a result. Otherwise the whole thing would be not of use to calculate.

It's a good point though, that you have raised!

Hope I am right!

For the question above, my answer is C :)
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by faraz_jeddah » Thu Sep 19, 2013 11:54 pm
vinay1983 wrote: Good to see you back. I changed the average from 3 to 2.25. Happens:)

Series gives us a concrete idea about the numbers we should consider. Like in the above question you have posted, if it would have been" terms, which are positive and in series (such as A.P or G.P) would gives us definite numbers to work with.Also I feel the no. of numbers is restricted by the average. In this case to get 3 as average we should have N numbers such that we get a integer as a result. Otherwise the whole thing would be not of use to calculate.

It's a good point though, that you have raised!

Hope I am right!

For the question above, my answer is C :)
Oh man I feel embarrassed now. The average is indeed 2.25.

Thanks Vinay!
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by theCodeToGMAT » Fri Sep 20, 2013 12:18 am
ANSWER [spoiler][C][/spoiler]
My Steps :
Statement 1:
( _ + _ + _ + _ + _ ) = 9

Statement 2:
( _ + _ + _ + _ + _ )/n = 3

( _ + _ + _ + _ + _ ) = 3n

Combining both
3n = 9 --> n = 3


Answer to your query:

You have made a small mistake in the second case

1,2,3,3 --> Sum = 9 BUT MEAN = 9/4=2.25
To have an average as 3 with "4 terms" you would need sum as 12; Doing so will affect statement 1
So, the series with 4 numbers is not Possible

hence, you Case 1: 0,1,8 is correct
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by Brent@GMATPrepNow » Fri Sep 20, 2013 6:02 am
faraz_jeddah wrote:If the terms of a sequence t1, t2, ....tn, what is the value of n?
1. The sum of the n terms is 3,124
2. The average (arithmetic mean) of the n terms is 4
For those of you who attempted the original question, here's one approach.

Target question: What is the value of n?

Statement 1: The sum of the n terms is 3,124
There are several sequences that satisfy this condition. Here are two:
Case a: the sequence is {0, 3124}, in which case n = 2
Case b: the sequence is {0, 0, 3124}, in which case n = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The average (arithmetic mean) of the n terms is 4
There are several sequences that satisfy this condition. Here are two:
Case a: the sequence is {4, 4}, in which case n = 2
Case b: the sequence is {4, 4, 4}, in which case n = 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We know: average = (sum of n numbers)/n
Statement 1 tells us the sum, and statement 2 tells us the average.
So, we get: 4 = 3124/n (which we COULD solve for n)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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