SAT Math Question of the Day

Q: If (a - 3)(3 + a) = 7, then what is a possible value for a?

1. 0
2. 1
3. 2
4. 3
5. 4

UNANSWERED.

The correct answer is E.

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 0,
(a - 3)(3 + a) = 7
(0 - 3)(3 + 0) = 7
(-3)(3) = 7
-9 = 7
Nope, choice A doesn't work. On to choice B: a is 1 ...
(a - 3)(3 + a) = 7
(1 - 3)(3 + 1) = 7
(-2)(4) = 7
-8 = 7
How about choice C: a is 2?
(a - 3)(3 + a) = 7
(2 - 3)(3 + 2) = 7
(-1)(5) = 7
-5 = 7
Could it be choice D: a is 3?
(a - 3)(3 + a) = 7
(3 - 3)(3 + 3) = 7
(0)(6) = 7
0 = 7
Well, there's only 1 option left, specifically where a is 4
(a - 3)(3 + a) = 7
(4 - 3)(3 + 4) = 7
(1)(7) = 7
7 = 7
IT WORKS!
So the answer is a is 4 or choice E.

Another way to solve it is algebraically:
(a - 3)(3 + a) = 7
(a - 3)(a + 3) = 7
a² - 9 = 7
a² = 16
a = 4 or -4
So, E is the correct answer.