Perceny change

[LiziS]

Hi!

Please explain why stat. 2 is sufficient. I guessed it right but still don't understand the explanation:

What is the maximum possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour.

(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

[Brent@GMATPrepNow]

What is the MAXIMUM possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour.

(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

Target question: What is the maximum possible number of chocolate bars per hour produced by a machine?

Statement 1: Currently, the machine produces 1,200 chocolate bars per hour.
No idea what the MAXIMUM rate is.
So, statement 1 is NOT SUFFICIENT

Statement 2: If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.
Let M = current maximum rate
So, we start with a rate of M/2
After we add 300, we get a new rate of M/2 + 300
This represents a 25% increase.

Percent increase = 100(new - old)/old
So, we can write: 100(M/2 + 300 - M/2)/(M/2) = 25
Note: At this point, we might recognize that we can solve this equation for M, in which case the statement is SUFFICIENT. However, if we're not convinced, we can continue solving...
Simplify: 100(300)/(M/2) = 25
Divide both side by 100: (300)/(M/2) = 1/4
Cross multiply: 4(300) = M/2
Simplify: 1200 = M/2
Solve: M = 2400
So, the maximum rate is 2400 chocolate bars per hour.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent