Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #46

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# A company makes and sells two products

A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are \$ 8.00 and \$ 9.50, respectively, and the selling prices per unit of P and Q are \$ 10.00 and \$ 13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than \$ 2,000.00?

### 1 Explanation

2

Jin Wu

Can someone help explain this problem?

OA says E (Statements 1 and 2 together are not sufficient), however,

if we let
X = the number of units sold for product P and
Y = the number of units sold for product Q

Then, we have:
X+Y=834
(\$10-\$8)X + (834-X)(\$13-\$9.50) > 2000
Which gives us:
X < 612.6
Y > 213.4

Since statement (1) says more units of P than units of Q were sold, does that not imply that X > Y, which makes the total profit

Oct 18, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Jin Wu :)
Let's look at the inequality (\$10-\$8)X + (834-X)(\$13-\$9.50) > 2000. When we simplify, we get
2919 - 1.5X > 2000. From here, we can test different values for X to see if we can definitively say that the left-hand side is greater or less than 2000. The only restriction we have is that X>Y. So the maximum value of X is 833, while the minimum value of X is 418:
X = 833 --> 2919 - 1.5(833) < 2000
X = 418 --> 2919 - 1.5(418) > 2000
As we can see, alone, Statement 1 is insufficient to determine whether the total profit was greater than 2000.
Now, let's consider the statements together. If P>Q and Q?100, then 100?Q?416 and 418?P?734. Let's use the equation above and the minimum and maximum values of P to evaluate the question:
X = 734 --> 2919 - 1.5(734) < 2000
X = 418 --> 2919 - 1.5(418) > 2000 (from above)
From here, we can see that the total profit could be greater than or less than 2000 when Q?100 and P>Q. So, we can say that combined Statements 1 and 2 are still insufficient.
I hope this helps!