SAT Math Question of the Day

Q: If (6 + a)(a - 6) = -27, then what is a possible value for a?

1. 1
2. 2
3. 3
4. 4
5. 5

UNANSWERED.

The correct answer is C.

A:

One way to do this problem is to just plug in the possible answers and see which one fits the equation.

Let's try choice A, where a is 1,
(6 + a)(a - 6) = -27
(6 + 1)(1 - 6) = -27
(7)(-5) = -27
-35 = -27
Nope, choice A doesn't work. On to choice B: a is 2 ...
(6 + a)(a - 6) = -27
(6 + 2)(2 - 6) = -27
(8)(-4) = -27
-32 = -27
How about choice C: a is 3?
(6 + a)(a - 6) = -27
(6 + 3)(3 - 6) = -27
(9)(-3) = -27
-27 = -27
IT WORKS!
So the answer is a is 3 or choice C.

Another way to solve it is algebraically:
(6 + a)(a - 6) = -27
(a + 6)(a - 6) = -27
a² - 36 = -27
a² = 9
a = 3 or -3
So, C is the correct answer.