Method-1:

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

i.e. Product of two consecutive Even Integers = 24
i.e. Either 4*(4+2) = 24
or -6*(-6+2) = 24

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

Method-2:

a(a + 2) = 24 and b(b + 2) = 24
i.e. \(a(a + 2) = b(b + 2)\)

i.e. \(a^2+2a - b^2-2b = 0 \)

i.e. \(a^2 - b^2 = -2(a-b)\)

i.e. \((a- b)*(a+b) = -2(a-b)\)

i.e. \((a+b) = -2\)

Answer: option B
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If a(a+2)=24 and b(b+2)=24
a(a+2)=b(b+2)
a^2+2a=b^2+2b
a^2-b^2=2b-2a
(a-b)(a+b)=2(b-a)
a+b=-2 (No need for smart numbers)

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

7. Algebra

• Theory
  Math : Algebra 101
  Algebra: Tips and hints
  FOIL on the GMAT: Simplifying and Expanding
  Factoring Quadratics
  Solving Quadratic Equations
  Using Algebra vs. Logic on GMAT Quant Questions
  
  • Questions
    Tough Algebra Set
    Algebra Ability Quiz by e-GMAT
    DS Questions
    PS Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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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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a(a + 2) = 24
a^2+2a-24 = 0
a = -6 or 4
same way b= -6 or 4
since a not equal to b
a+b must be -6+4 = -2
answer -2

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
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Hi everyone, just want to confirm my thinking here.

If a(a+2)=24, can't we just say that a=0 or -2? Thus the same for b, which a+b gives us -2. No need to solve the long way, or am I missing something?

Does a = 0 or a = -2 satisfy a(a + 2) = 24. Foe both of these values a(a + 2) is 0, NOT 24.

7. Algebra

• Theory
  Math : Algebra 101
  Algebra: Tips and hints
  FOIL on the GMAT: Simplifying and Expanding
  Factoring Quadratics
  Solving Quadratic Equations
  Using Algebra vs. Logic on GMAT Quant Questions
  
  • Questions
    Tough Algebra Set
    Algebra Ability Quiz by e-GMAT
    DS Questions
    PS Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Hi,

I solved this question in the following way:
a(a+2)=24 and b(b+2)=24

Simplifying this, we get:
a^2+2a=24 and b^2+2b=24

Now, since both the expressions are equal to 24, we get:
a^2+2a=b^2+2b
a^2-b^2=2b-2a

If you see the LHS, it's in the form of a^2-b^2, which is equal to (a+b)(a-b).

Hence, (a+b)(a-b)=2(b-a)

I factored 2 out on the RHS. Note, b-a can also be written as -1(a-b). So, we now get:

(a+b)(a-b)=2*-1(a-b)
(a+b)(a-b)=-2(a-b)

(a-b) gets cancelled both both on LHS and RHS.

a+b = -2

Hope this is helpful!

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
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Answer: Option B

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