RiyaR wrote:If S is the sum of the first n positive integers, what is the value of n?
1) S < 20
2) S² > 220
Target question: What is the value of n?
Given: S is the sum of the first n positive integers
Statement 1: S < 20
There are several values of n that satisfy this condition. Here are two:
Case a:
n = 2. Here, S = 1 + 2 = 3, which is less than 20
Case b:
n = 3. Here, S = 1 + 2 + 3 = 5, which is less than 20
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: S² > 220
There are several values of n that satisfy this condition. Here are two:
Case a:
n = 50. Here, S = 1 + 2 + .... + 50, so S² = is definitely bigger than 220.
Case b:
n = 51. Here, S = 1 + 2 + .... + 51, so S² = is definitely bigger than 220.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
USEFUL FORMULA: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2
Let's examine a few possible values of n and the subsequent values of S and S²
n = 4. Applying the formula, we see that S =
4(
4+1)/2 = 10
So, S = 10 and S² = 100
This meets the statement 1 condition that S < 20, but it does NOT meet the statement 2 condition that S² > 220
So,
n cannot equal 4.
n = 5. Applying the formula, we see that S =
5(
5+1)/2 = 15
So, S = 15 and S² = 225
This meets the statement 1 condition that S < 20, AND it meets the statement 2 condition that S² > 220
So,
n COULD EQUAL 5.
n = 6. Applying the formula, we see that S =
6(
5+1)/2 = 21
So, S = 21 and S² = 441
This does NOT meet the statement 1 condition that S < 20, but it meets the statement 2 condition that S² > 220
So,
n CANNOT equal 6.
As you can see, any value of n greater than 5 will not meet the statement 1 condition.
So,
it MUST be the case that n = 5
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
