If the terms of a sequence are t1, t2, t3, ..., tn, what is the value

1. sum of n terms is 3124
It means that t1+...tn=3124=>insuff
2. t1+...tn=4n=> insuff

Combine 1 &2 : 4n=3124 => suff

C is the best answer

I choose E.

1. n(n+1)/2 = 3124 => solving for n gives -3 or 2. Therefore 2. Sufficient
2. n(n+1)/2n = 4 => solving for n gives 0 or 7. Therefore 7. Sufficient

Not really sure where you're going here. First, if you think each statement is sufficient, you should be choosing D, not E. You also seem to be assuming that the sequence is a sequence of consecutive integers beginning from 1 - that's the only situation where you could use the "sum = n(n+1)/2" formula. You aren't told what kind of sequence this is, so you can't use any formula for the sum here. Finally, I don't understand how you arrived at the solutions -3 and 2 from the equation n(n+1)/2 = 3124.

prosper's solution is correct.

Question Stem: What is n?

From Statement 1:The sum of n terms is 3124
=>t1+t2+....+tn=3124----(1)
We cannot find the value of n by this. So insufficient.

From Statement 2:The average (arithmatic mean) of n terms is 4
=>(t1+t2+....+tn)/n=4------(2)
We cannot find the value of n by this. So insufficient.

Combining (1) and (2) by substituting (1) in (2) we get,
3124/n=4....=>n=781
Hence the answer has to be C

Hi, sorry for digging this up again, but nowhere in the question stem do they mention that the series is an evenly spaced sequence. I chose E based on that logic. Are we to assume that any sequence is evenly spaced?

Given : The terms t1,t2,t3,t4...., tn are in sequence. But we don't know which sequence this is
DS : value of n

Statement 1: t1 + t2 + t3 +t4 +.... + tn = 3124
NOT SUFFICIENT

Statement 2: (t1 + t2 +t3 + t4 +... + tn )/n = 4
-> (t1 + t2 +t3 + t4 +... + tn ) = 4n
NOT SUFFICIENT

Combined : 4n = 3124
SUFFICIENT

Answer C

The sum of the n terms is 3,124.

Since we don’t know anything about each individual term, we can’t determine the number of terms in the sequence. Statement one alone is not sufficient.

Statement Two Only:

The average of the n terms is 4.

Since we don’t know anything about each individual term, we can’t determine the number of terms in the sequence. Statement one alone is not sufficient.

Statements One and Two Together:

Since sum = quantity x average, we have:

3,124 = n x 4

n = 3,124/4 = 781

Answer: C

ScottTargetTestPrep Bunuel VeritasKarishma

Nothing has been mentioned whether the sequence starts with a positive number or a negative number.
If some part of the sequence is negative then how can we use its sum and average to find the total number of terms?

Irrelevant whether there are negative numbers or not. Average takes it into account.

Avg of 2, 3, 4 = 3
Avg of -1, 0, 1, 2, 3, 4 = 1.5 (not 3)

Avg = Sum/ Number of terms

The sum is the same in both cases but number of terms are different. This gives us a diff average.
When you divide the sum by avg, you get the actual number of terms.

But, good thinking. This is how you will be able to clear your concepts.

As long as the average is not zero, dividing the sum by the average will give us the number of terms in the sequence.
Let's consider a single term of 20, where both the sum of the terms and the average is equal to 20. Here, the number of terms is 20/20 = 1.

Now, let's consider -19, -18, -17, ... , 18, 19, 20. Since every negative term will cancel a corresponding positive term, the sum of this sequence is also 20. This is a sequence of consecutive integers, so the average of the entire sequence is equal to the average of the first and last terms: [20 + (-19)]/2 = 1/2. Notice that dividing the sum by the average suggests 20/(1/2) = 40 terms. Indeed, the number of terms in this sequence is 20 - (-19) + 1 = 40.

As we can see, it does not matter whether the sequence contains any negative terms or not. Dividing the sum by the average will always give us the number of terms.

It's not specified that the series is an AP or GP or any other sequence. How can we make this assumption? The only thing that atleast shows that it's arithmetic sequence is the arithmetic mean, still we can find the AM of GPs as well.

Anyone else having the same doubt?

We aren't told what kind of sequence this is. It could be AP, GP or any other. The fact that we are given the average (arithmetic mean) of the sequence does not necessarily mean that the sequence is an AP. All sequences of numbers have the average. The formula:

(The average (arithmetic mean)) = (the sum of the terms)/(the number of the terms)

is true for any kind of sequence.

P.S. Your doubt is also addressed here: https://gmatclub.com/forum/if-the-terms ... l#p1893924

If the terms of a sequence are t1, t2, t3, ..., tn, what is the value of n ?

(1) The sum of the n terms is 3,124.
Here in this question, we don't have any idea about the series, whether its arithmetic / geometric progression or of a different pattern.
So the sum alone will not be sufficient to find the number of terms.

(2) The average (arithmetic mean) of the n terms is 4.
Avg = total sum of the series/no of terms = 4
By using statement 2 alone, we will not be able to find the number of terms as we don't know about the sum.

But if you combine statement 1 and 2, Its given that sum = 3,124 and average = 4.
With these 2 info, we can definitely find the value of n as avg =sum/n

Option C is the answer.

Thanks,
Clifin J Francis,
GMAT SME

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.