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If S is the sum of the first n positive integers, what is the value of n ?

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by BTGModeratorVI » Wed Feb 26, 2020 4:23 pm

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If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) S^2 > 220

Answer: C
Source: Official Guide
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Re: If S is the sum of the first n positive integers, what is the value of n ?

by Jay@ManhattanReview » Wed Feb 26, 2020 11:41 pm
BTGModeratorVI wrote: ↑
Wed Feb 26, 2020 4:23 pm
 If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) S^2 > 220

Answer: C
Source: Official Guide
Certainly, each statement alone is insufficient. Let's combine them.

(1) and (2) together

From, (2), we have s^2 > 220 => s > 14... Since s is an integer, we have s ≥ 15.

Thus, from both statements together, we have 15 ≥ s > 20.

Taking the integers 1, 2, 3, 4, 5 and 6, we see that the sum of the first 5 is 15 and the sum of the first 6 is 21, not qualified. Thus, n = 5. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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Re: If S is the sum of the first n positive integers, what is the value of n ?

by Brent@GMATPrepNow » Fri Feb 28, 2020 9:34 am
BTGModeratorVI wrote: ↑
Wed Feb 26, 2020 4:23 pm
 If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) S^2 > 220

Answer: C
Source: Official Guide
Given: S is the sum of the first n positive integers

Target question: What is the value of n ?

Statement 1: S < 20
If n = 5, then S = 1 + 2 + 3 + 4 + 5 = 15
If n = 6, then S = 1 + 2 + 3 + 4 + 5 + 6 = 21
Since S < 20, we know that n < 6
This means n COULD equal 1, 2, 3, 4, or 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: S² > 220
Let's test some values.
If n = 4, then S = 1 + 2 + 3 + 4 = 10, which means S² = 10² = 100
If n = 5, then S = 1 + 2 + 3 + 4 + 5 = 15, which means S² = 15² = 225
Since S² > 220, we know that n > 4
This means n COULD equal 5 or 6 or 7 or 8 or .....
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that n < 6
Statement 2 tells us that n > 4
Combine the inequalities to get: 4 < n < 6
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
Brent Hanneson - Creator of GMATPrepNow.com
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