Data Sufficiency

Sak32 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 3124
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