BTGModeratorVI wrote: ↑Fri Jul 03, 2020 7:11 am
If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n = −n
Answer:
D
Source: Veritas Prep
Target question: Is n positive?
Given: In is an integer
Statement 1:(2n+1)/(n+1) is an integer
Rewrite as: (n+1+
n)/(n+1) is an integer
Rewrite as: (n+1)/(n+1) +
n/(n+1) is an integer
Or... 1 +
n/(n+1) is an integer
This means that n/(n+1) is an integer
How can this be? How can some number divided by a number that's 1 greater be an integer?
This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0
In other words,
n is NOT positive
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: n=−n
Add n to both sides to get: 2n = 0
Divide both sides by 2 to get: n = 0
So,
n is NOT positive
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
