VJesus12 wrote: ↑Thu Nov 04, 2021 5:08 am
If \(n\) is an integer, is \(n\) even?
(1) \(n^2 - 1\) is an odd integer.
(2) \(3n + 4\) is an even integer.
Answer:
D
Source: GMAT Paper Tests
Some important rules:
1. ODD +/- ODD = EVEN
2. EVEN +/- ODD = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN
Target question: Is integer n EVEN?
Statement 1: n² - 1 is an odd integer
n² - 1 = (n + 1)(n - 1)
So, statement 1 is telling us that (n + 1)(n - 1) = ODD
From
rule #4 (above), we can conclude that BOTH (n + 1) and (n - 1) are ODD
If (n + 1) is ODD, then
n must be EVEN (since 1 is ODD, we can apply
rule #2 to conclude that n is EVEN)
If (n - 1) is ODD, then
n must be EVEN (by
rule #2 )
So,
the answer to the target question is YES, n is even
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 3n + 4 is an even integer
In other words, (3n + EVEN) is EVEN
From
rule #3, we can conclude that 3n is EVEN
Since 3 is odd, we can write: (ODD)(n) = EVEN
From
rule #5, we can conclude that
n is EVEN
So,
the answer to the target question is YES, n is even
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
