Data Sufficiency

vinay1983 wrote:What is the profit percentage obtained by Chris, a bookseller, from the sale of a new book?

1) Chris sold the book for $40
2) If Chris had sold the book at two thirds the price at which he actually sold it then he would have incurred a loss of 22%

Target question: What is the profit percentage obtained from the sale of a new book?

Let W = wholesale price that Chris paid for the book
Let R = retail price that Chris charged for the book

IMPORTANT: Percent profit = 100(R - W)/W
= (100R - 100W)/W
= 100R/W - 100W/W
= 100R/W - 100

So, as you can see, to find the percent profit, we need only determine the value of R/W (at which point, we are guaranteed to find the percent profit)

Rephrased target question: What is the value of R/W?

Statement 1: Chris sold the book for $40
So, R = 40, but we don't know the value of W.
As such, we cannot determine the value of R/W
Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If Chris had sold the book at two thirds the price at which he actually sold it then he would have incurred a loss of 22%
So, the retail price was (2/3)R and the profit was -22%
Call up profit formula: 100R/W - 100 = percent profit
Plug in values: 100(2/3)R/W - 100 = -22
Add 100 to both sides: 100(2/3)R/W = 78
Divide both sides by 100: (2/3)R/W = 78/100
Multiply both sides by 3/2: R/W = (78/100)(3/2)

STOP

As we can see, statement 2 allows us to determine the value of R/W (which will guaranteed our ability to find the percent profit). We need not find the actual value of R/W. We need only recognize that statement 2 provides sufficient information to determine this value.
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent