If a + c b, then 4a² - (a + b - c)²/a-b+c=

Question

If a + c ≠ b, then  \frac{{4a2 - (a + b - c)2}}{{a - b + c}} =

A) a - b - c
B) a + b - c
C) 3a - b - c
D) 3a + b + c
E) 3a + b - c

Kurtosis · Accepted Answer

Let a = b = c = 1 -->  a + c 
eq {b}

Substitute a, b and c in the given equation --> (4(1) - (1 + 1 - 1)^2)/(1 - 1 + 1) = 4 - 1 = 3

When a, b and c are substituted in the given options we must get the answer as 3

A) a - b - c = -1 --> Incorrect
B) a + b - c = 1 --> Incorrect
C) 3a - b - c = 1 --> Incorrect
D) 3a + b + c = 5 --> Incorrect
E) 3a + b - c = 3 --> Correct

Answer: E

sjavvadi · Answer

Looking at the numerator:

4a^2-(a+b-c)^2 = (2a)^2-(a+b-c)^2 = (2a+a+b-c)(2a-a-b+c) = (3a+b-c)(a-b+c).

Therefore, the total term = (3a+b-c)(a-b+c)/(a-b+c) = 3a+b-c

Ans is (E)

BrentGMATPrepNow · Answer

The key to answering this question is recognizing that we have a  difference of squares  hiding in the given algebraic expression

We know this because  4a^2  can be re-written as  (2a)^2 , which means  4a^2  is a SQUARE. 
Likewise,  (a + b - c)^2  is obviously a SQUARE.

So the original expression can be re-written as:  \frac{{(2a)^2 - (a + b - c)^2}}{{a - b + c}} =

We can factor a difference of squares as follows:  x^2 - y^2 = (x + y)(x - y)

So, take:  \frac{{(2a)^2 - (a + b - c)^2}}{{a - b + c}}

Factor the numerator to get:  \frac{{  }}{{a - b + c}}

Simplify the numerator to get:  \frac{{(3a + b - c)(a -b+c)}}{{a - b + c}}

Since we have  (a -b+c)  in the numerator and denominator, they cancel out to get:  3a + b - c

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a + c b, then 4a² - (a + b - c)²/a-b+c=

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a + c b, then 4a² - (a + b - c)²/a-b+c=

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards