If a( a + 2) = 24

boomgoesthegmat wrote:If a( a + 2) = 24 and b( b + 2) = 24, where a does not equal b, then a + b =

A) -48
B) -2
C) 2
D) 46
E) 48

OA: B

Given: a(a + 2) = 24
Expand: a² + 2a = 24
Rearrange: a² + 2a - 24 = 0
Factor: (a + 6)(a - 4) = 0
So, a = -6 OR a = 4

Given: b(b + 2) = 24
Expand: b² + 2b = 24
Rearrange: b² + 2b - 24 = 0
Factor: (b + 6)(b - 4) = 0
So, b = -6 OR b = 4

Since we're told that a ≠ b, we know that one value (a or b) is -6 and the other value is 4
So, a + b = (-6) + 4 = -2

Answer: B

Cheers,
Brent

Hi All,

This prompt gives us two equations to work with:

A(A+2) = 24
B(B+2) = 24

And we’re told that A is NOT equal to B. We’re asked for the sum of A+B. At first glance, the two equations appear to be identical (meaning that A would equal B). However, since we’re told that those two values are NOT equal to one another, then we need to be thinking about how there could be two DIFFERENT answers to those two equations.

You can certainly approach these equations by setting up Quadratics, but if you’re comfortable with basic Arithmetic, then you don’t need to do any ‘step-heavy’ math to answer this question.

Since A and (A+2) differ by 2, can you think of two numbers – that differ by 2 – that when multiplied together will equal 24….? You probably learned basic multiplication when you were 7 or 8 years old, so it shouldn’t take much effort to figure out that the numbers 4 and 6 fit that description: (4)(4+2) = 24. Thus, A = 4.

Next, what else could we multiply together to get 24? As a hint, the prompt did NOT tell us that the variables had to be positive numbers…? The numbers -4 and -6 also fit that description: (-6)(-6 + 2) = (-6)(-4) = 24. Thus, B = -6

The value of A+B is…

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich