MadanNyp wrote:

By selling two articles for Rs X, Joey gains 30% on one and loses 30% on the other. What is the net profit/loss percentage suffered/gained by Joey?

A. loss of 15%

B. loss of 9%

C. no profit no loss

D. profit of 9%

E. profit of 15%

Dear

MadanNyp,

I'm happy to respond.

My friend, understand that this question is not written with the clarity typical of GMAT question. In particular, it's not 100% clear whether the price stated, Rs X, is the value

before the percents gain & loss, or whether it is the price received,

after the gain & loss. If the former is the case, it's a very easy question. I believe the latter is the case, and that's a more challenging question. That's the version I'll solve here.

Let's assume that Joey sold these two items, each for the same price. For one item, the sale at that price represented a 30% gain over its value. For the other, the sale at that same price represented a 30% loss compared to its value. What is the total percent loss?

First, a conceptual approach. Let's say that the sale price for both items is Rs. 1000. The value of the first item is some P < 1000, and 1000 is a 30% increase on P. The value of the second item is some Q > 1000, and a 30% decrease in Q equals 1000. We gained 30% of P and lost 30% of Q. We know that Q > P, so 30% of Q is much larger than 30% of P. Therefore, the loss was greater than the gain, and there is net loss in the sale. Without any calculations, we see that either (A) or (B) has to be the answer. That's important to understand.

Now, let's think about calculating the exact numerical answer. Using those variables, we can create the equations

P*1.3 = X

Q*0.7 = X

Notice that 1.3 is the

multiplier for a 30% increase and 0.7 is the multiplier for a 30% decrease.

Notice that to solve for P & Q, we will need to divide by 0.7 and 1.3. This means that a well-chosen value of X should be divisible by both 7 and 13. Let's just use 91 = 7*13.

We will say that X = 91. Joey sold each item for the same price, Rs 91.

The first item was worth P, and P*1.3 = 91. Thus, P = 91/1.3 = 70. The first item was worth Rs. 70 and sold for Rs 91, a 30% increase.

The second item was worth Q, and Q*0.7 = X. Thus, Q = 91/0.7 = 130. The second item was worth Rs. 130 and sold for Rs 91, a 30% loss.

The net value before the sales was P + Q = 200. The net gain from the two sales was 91 + 91 = 182. This is a percent loss

Percent loss = (200 - 182)/200 x 100% = 18/200 x 100% = 9/100 x 100% = 9%

The total loss is 9%.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)