grandh01 wrote:If S is the sum of the first n positive
integers, what is the value of n ?
(1) S < 20
(2) S^2 > 220

OA is C

Target question: What is the value of n?

Statement 1: S < 20
This statement yields some contradictory cases. Here are two:
case a: n=2 to get S = 1+2 = 3 < 20
case b: n=3 to get S = 1+2+3 = 6 < 20
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: S^2 > 220
Since S must be a positive integer, this statement essentially tells us that S>14 (since 14^2=196 and 15^2=225)
This statement yields some contradictory cases. Here are two:
case a: n=5 to get S = 1+2+3+4+5 = 15 > 14
case b: n=6 to get S = 1+2+3+4+5+6 = 21 > 14
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Statements 1& 2:
The combined statements tell us that 14 < S < 20
Let's examine some sums in this range.
- n=4 to get S = 1+2+3+4 = 10 (doesn't fit into range)
- n=5 to get S = 1+2+3+4+5 = 15 (WORKS)
- n=6 to get S = 1+2+3+4+5+6 = 21 (doesn't fit into range)
So, the combined statements tell us that n must equal 5.
SUFFICIENT

Answer = C

Cheers,
Brent