SAT Math Question of the Day

Math Category: Algebra:

Q: If (6 + a)(a - 6) = 45, then what is a possible value for a?

  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

UNANSWERED.

The correct answer is B.

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 8,
(6 + a)(a - 6) = 45
(6 + 8)(8 - 6) = 45
(14)(2) = 45
28 = 45
Nope, choice A doesn't work. On to choice B: a is 9 ...
(6 + a)(a - 6) = 45
(6 + 9)(9 - 6) = 45
(15)(3) = 45
45 = 45
IT WORKS!
So the answer is a is 9 or choice B.

Another way to solve it is algebraically:
(6 + a)(a - 6) = 45
(a + 6)(a - 6) = 45
a2 - 36 = 45
a2 = 81
a = 9 or -9
So, B is the correct answer.