SAT Math Question of the Day

Math Category: Algebra:

Q: If (x - 5)(x + 5) = 11, then what is a possible answer for x?

  1. -10
  2. -8
  3. -6
  4. -4
  5. -2

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 x is -10,
(x - 5)(x + 5) = 11
(-10 - 5)(-10 + 5) = 11
(-15)(-5) = 11
75 = 11
Nope, choice A doesn't work. On to choice B, x is -8 ...
(x - 5)(x + 5) = 11
(-8 - 5)(-8 + 5) = 11
(-13)(-3) = 11
39 = 11
Still not a match. Let's try choice C, where x is -6 ...
(x - 5)(x + 5) = 11
(-6 - 5)(-6 + 5) = 11
(-11)(-1) = 11
11 = 11
IT WORKS!
So the answer is x is -6 or choice C.

Another way to solve it is algebraically:
(x - 5)(x + 5) = 11
x2 - 25 = 11
x2 = 36
x = 6 or -6
So, C is the correct answer.