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.

(2) The average (arithmetic mean) of the n terms is 4.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

-Answer is C...I don't understand why? Is this question implying that the numbers are consecutive integers? I have a lot fo trouble with sequences. Any tips or recommendations? Thanks!

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You should never assume that a sequence has any particular 'structure' unless the question explicitly tells you it does. A sequence is just a list of numbers in order, and can have any structure at all. We can't assume we have, say, consecutive integers here.

We want to know what n is, or in other words, how many things are in this sequence. From Statement 1, we only know all the terms add up to 3124. We could have any number of terms at all - for example the sequence could have two terms:

1, 3123

or it could have 3124 terms that all equal 1:

1, 1, 1, 1, 1, 1, 1, 1, .... , 1

among an infinitude of possibilities.

Statement 2 tells us that the average of the entire sequence is 4, but that doesn't help us find the number of terms - we could again have two terms that add to eight, say:

4, 4

or we could have one thousand terms that add up to 4000:

4, 4, 4, 4, 4, 4, ..... , 4

and again we have infinitely many possibilities.

Using both Statements, we know the sum of the sequence is 3124, and the average of the sequence is 4. By the definition of an average,

average = sum/n

so in this question

4 = 3124/n

4n = 3124

n = 3124/4

and we can find n, the number of terms, using both statements. Notice that we still don't know what the sequence is -- there's no reason to think we have consecutive integers, for example -- but we can still find the number of terms from the information provided.

We want to know what n is, or in other words, how many things are in this sequence. From Statement 1, we only know all the terms add up to 3124. We could have any number of terms at all - for example the sequence could have two terms:

1, 3123

or it could have 3124 terms that all equal 1:

1, 1, 1, 1, 1, 1, 1, 1, .... , 1

among an infinitude of possibilities.

Statement 2 tells us that the average of the entire sequence is 4, but that doesn't help us find the number of terms - we could again have two terms that add to eight, say:

4, 4

or we could have one thousand terms that add up to 4000:

4, 4, 4, 4, 4, 4, ..... , 4

and again we have infinitely many possibilities.

Using both Statements, we know the sum of the sequence is 3124, and the average of the sequence is 4. By the definition of an average,

average = sum/n

so in this question

4 = 3124/n

4n = 3124

n = 3124/4

and we can find n, the number of terms, using both statements. Notice that we still don't know what the sequence is -- there's no reason to think we have consecutive integers, for example -- but we can still find the number of terms from the information provided.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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We are given the following sequence: t(1), t(2), t(3),...,t(n).simpm14 wrote: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.

(2) The average (arithmetic mean) of the n terms is 4.

We are asked to find the value of n, or, in other words, we need to determine the number of terms in the sequence.

Statement One Alone:

The sum of the n terms is 3,124.

Knowing only that the sum of the n terms is 3,124 is not enough information to determine the value of n. There could be just two terms, such as 3000 and 124, or there could be 3,124 terms, each equal to 1. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The average (arithmetic mean) of the n terms is 4.

Knowing only that the average of the n terms is 4 is not enough information to determine the value of n. There could be just two terms, such as 2 and 6, or there could be a thousand terms that add up to 4000. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the two statements, we know that the sum of the n terms is 3,124 and the average of the terms is 4. Since average = sum/quantity, quantity = sum/average; thus:

quantity = 3,124/4

quantity = 781

n = 781

Answer: C

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simpm14 wrote: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.

(2) The average (arithmetic mean) of the n terms is 4.

**Target question:**

**What is the value of n?**

In other words, "How many terms are in the sequence?"

**Statement 1: The sum of the n terms is 3124**

There are many sequences that satisfy this condition. Here are two:

Case a: the sequence is {3124}, in which case n = 1

Case b: the sequence is {0, 3124}, in which case n = 2

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 many 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**

IMPORTANT: average (arithmetic mean) of n terms = (sum of all terms)/n

Statement 1 tells us that the sum = 3124

Statement 2 tells us that the average = 4

So, 4 = 3124/n

We can solve this to get n = 781

*Aside: Of course we'd never actually solve the equation since we need only determine whether we have enough information to answer the target question*

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Brent

The Original sequence T1, T2, T3.......Tn can be arithmetic progression , geometric progression or may not be in any progression at all.simpm14 wrote: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.

(2) The average (arithmetic mean) of the n terms is 4.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

-Answer is C...I don't understand why? Is this question implying that the numbers are consecutive integers? I have a lot fo trouble with sequences. Any tips or recommendations? Thanks!

In (1) Sum of n Terms, is given as 3124, with this information we cannot conclude if the original sequence is AP, GP or any random sequence at all

In (2) It is explicitly mentioned that average (arithmetic mean is of n terms is 4. Hence we can conclude that the original sequence is in Arithmetic progression AP. having only mean will not help us identify the nth terms of sequence.

Now combining 1 and 2, we have sum as 3124, mean of AP as 4.

nth term of AP = Sum of terms /Mean = 3124/4 = 781. There are 781 terms in the sequence . Mean being 4, there will be lot negative numbers in the sequence .

Hence is C.