GMATPrepNow wrote:
If a, b, and c are consecutive integers such that a < b < c, which of the following CANNOT be the value of (b² – a²)(c² – b²)?
(A) 323
(B) 483
(C) 575
(D) 613
(E) 899
Great solution, maxx0811!
My solution is similar to yours, but I didn't notice that I could save a bit of time by assigning variables similar to the way in which you assigned to the variables.
Here's how I approached the question:
Since a, b, and c are consecutive integers and a < b < c, we know that...
a = a
b = a + 1
c = a + 2
So, (b² – a²)(c² – b²) = [(a + 1)² - a²][(a + 2)² - (a + 1)²]
= [a² + 2a + 1 - a²][(a² + 4a + 4) - (a² + 2a + 1)]
= [2a + 1][2a + 3]
= 4a² + 8a + 3
=
4(a² + 2a) + 3
=
3 greater than some multiple of
4Now let's check the answer choices....
(A) 323
320 is a multiple of
4, which means 323 is
3 greater than a multiple of
4Keep A
(B) 483
480 is a multiple of
4, which means 483 is
3 greater than a multiple of
4Keep B
(C) 575
572 is a multiple of
4, which means 575 is
3 greater than a multiple of
4Keep C
(D) 613
610 is NOT a multiple of
4, which means 613 is NOT
3 greater than a multiple of
4Voila!
Answer: D
Cheers,
Brent
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