Brent@GMATPrepNow wrote:Set T consists of 100 consecutive odd integers. If k is an integer, which of the following CANNOT equal the median of set T?
A) k² - k - 6
B) k² + 8k + 15
C) 4k² + 4k + 1
D) k³ - 4k² - k
E) 3k³ - 27k²
Answer:
C
Source:
www.gmatprepnow.com
Estimated difficulty level: 650-700
Cheers,
Brent
One more approach:
If Set T COULD look like this: { -99, -97 ..... -3, -1, 1, 3......97, 99 }, in which case the median =
zero
We can see that answer choices A, B, D and E could equal
zero, so we can ELIMINATE them.
Here's what I mean:
A) k² - k - 6 = (k + 2)(k - 3). So, answer choice A could equal
zero if k = -2 or k = 3. ELIMINATE A
B) k² + 8k + 15 = (k + 3)(k + 5). So, answer choice B could equal
zero if k = -3 or k = -5. ELIMINATE B
D) k³ - 4k² - k. If k = 0, then answer choice D could equal
zero . ELIMINATE D
E) 3k³ - 27k². If k = 0, then answer choice E could equal
zero. ELIMINATE E
What about answer choice C??
C) 4k² + 4k + 1 = (2k + 1)(2k + 1), so answer choice C could equal
zero if k = -1/2. HOWEVER, we're told that
k is an integer.
So, 4k² + 4k + 1 CANNOT equal
zero.
In fact, if k is an integer, we can see that 4k² + 4k + 1 must be ODD, and as regor60 noted, the median of set T must be EVEN.
Answer: C
Cheers,
Brent
