If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b =

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a^2+2a-24=0 b^2+2b-24=0
(a+6)(a-4) (b+6)(b-4)
a=-6, 4 b= -6, 4

A=-6 b=4

(-6)+4=-2

i.e. if a = 4 then b = -6
or if a = -6 then b = 4

But in each case a+b = -6+4 = -2

Answer: option B

a(a+2) = 24--eq1
b(b+2) = 24 --eq2

this can be written as X(x+2) = 24 where a,b are roots of this equation.
We just need to find sum of roots for the equation x^2+2x-24=0
Sum of roots of a quadratic equation is -(coefficient of X)/(coefficient of x^2) = -2

a(a + 2) = 24 and b(b + 2) = 24
=> a, b must be integers and if a is -6 or 4, b will be 4 and -6 respectively
=> a+b = -2

Ans: B

I did the long way:
a^2 +2a = 24
b^2 +2b = 24
these 2 equations are equal
a^2+2a=b^+2b
substract
a^2+2a-b^2-2b = 0
a^2 - b^2 can be written as (a+b)(a-b) +2a-2b = 0
factor 2a-2b-> +2(a-b)
rewrite:
(a+b)(a-b)=-2(a-b)
divide by (a-b) and get a+b = -2

as RHS is equal so we can equate LHS of both the eqns.

\(a^2 + 2a = b^2 + 2b\)
\(a^2 - b^2 = 2(b-a)\)
\((a+b)(a-b) = 2(b-a)\)
\(a+b =-2\)

a(a+2)=24....(i)
b(b+2)=24....(ii)
from (i) & (ii)
a(a+2)=b(b+2)
or a^2-b^2=-2(a-b)
or, (a+b)(a-b)=-2(a-b)
or, (a+b)=-2

ANS:B

we can do in this way also

i.e. if a = 4 then b = -6
or if a = -6 then b = 4

But in each case a+b = -6+4 = -2

Answer: option B
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Let’s solve for a and b.

a(a + 2) = 24

a^2 + 2a - 24 = 0

(a + 6)(a - 4) = 0

a = -6 or a = 4

and

b(b + 2) = 24

b^2 + 2b - 24 = 0

(b + 6)(b - 4) = 0

b = -6 or b = 4

Since a ≠ b, if a = -6, then b = 4, and if a = 4, then b = -6. Either way, we see that a + b is equal to -2.

Answer: B

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:

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

Video solution from Quant Reasoning:
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Answer: Option B

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a(a + 2) = 24 and b(b + 2) = 24

a^2 +2a-24 =0 & b^2+2b-24=0

if a = 4 then b = -6
or if a = -6 then b = 4

But in each case a+b = -6+4 = -2

What am I doing wrong here?

a(a + 2) = 24
a^2 +2a-24 =0
a(a+12)-2(a+12)=0
(a+12) (a-2)=0
That gives following values:
a = -12 or a = 2

& following the same b gives the following values:
b(b + 2) = 24
b^2+2b-24=0
b(b+12)-2(b+12)=0
(b+12) (b-2)=0
b = -12 then b =2

But in each case a+b = -12+2 = -10
Or a+b=2+(-10)=-10

I am confuessed here. Please help.

Hi Pamela,

There's an error in how you set up your Quadratics (and if you FOIL your calculations back out, you will see that they do NOT match the original equations that you are given).

a^2 +2a-24 =0

actually factors down into...
(a + 6)(a - 4) = 0
a = -6 or +4

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com

can you please explain how it became minus 2 at the end. where did that minus sign come from