Target question: What is the value of n?AAPL wrote:Manhattan Prep
The sum of \(n\) consecutive positive integers is 45. What is the value of \(n\)?
1) \(n\) is even.
2) \(n < 9\)
OA E
Given: The sum of n consecutive positive integers is 45.
Let's see what this given information tells us.
Some possible scenarios:
- the numbers are 1,2,3,4,5,6,7,8,9
- the numbers are 5,6,7,8,9,10
- the numbers are 7,8,9,10,11
- the numbers are 14,15,16
- the numbers are 22,23
At this point, we might already see that the answer is E.
To see why, let's go straight to . . .
Statements 1 and 2 combined
There are two sets of consecutive numbers that meet the two given conditions:
Case a: the numbers are {5,6,7,8,9,10} in which case n = 6
Case b: the numbers are {22,23} in which case n = 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
