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

Question

(A) −48
(B) −2
(C) 2
(D) 46
(E) 48

alphaseeker · Accepted Answer

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)

GMATinsight · Answer

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

Bunuel · Answer

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.

pmklings · Answer

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

shakticnb · Answer

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

raviCh · Answer

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

camlan1990 · Answer

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

mvictor · Answer

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

M3sSiaH · Answer

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

jasimuddin · Answer

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

mindi · Answer

we can do in this way also :-D

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 _________________ Please award kudos if you like my explanation. Thanks

ScottTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=bdlRZASE37w

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=6eFedTia85Q

Mraax · Answer

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

Pamela · Answer

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.

EMPOWERgmatRichC · Answer

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

shwetasood · Answer

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

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

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

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