A Company Makes and Sells Two Products, P and Q GMAT Data Sufficiency

Question: 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 835 units of these products. Was the total profit on these items more than $2,000?

1. During the month, more units of P than units of Q were sold
2. During the month, atleast 100 units of Q were sold

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Approach Solution (1):

Profit on per unit of P = $2
Profit on each unit of Q = $3.50
The company sold a total of 834 units
If all units were P, revenue = 834 * 2 = 1668
If all units were Q, revenue = 834 * 3.5 = more than 2400
Had they been split evenly between P and Q, it would have sold 417 units of each
This would give a revenue of 417 * 2 + 417 * 3.5 = 834 + (something above 1200) = more than 2000
S1: During this month, more units of P than units of Q were sold
There were more units of P. if say there were 418 units of P and 416 of Q, the revenue would remain more than 2000. If there were mostly P sold, revenue would go below 2000.
Hence not sufficient
S2: During this month, atleast 100 units of Q were sold.
100 units of Q give an additional 100 * 1.5 = 150 dollars only. So a split such as 734 – 100 would give revenue of 1668 + 150 (less than 2000)
Again P and Q split could be anything such as 417 – 417 in which case revenue would be more than 2000
Hence not sufficient
Using both the statements, the split of P-Q can be 418 – 416 (more than 200 revenue) or 734 – 100 (revenue less than 2000)

Correct option: E

Approach Solution (2):

Profit per unit of P = 10 – 8 = 2
Profit per unit of Q = 13 – 9.5 = 3.5
Let the number of units of P sold = p
Number of units of Q sold = q
Total number of units sold, p + q = 834
Is 2p + 3.5q > 2000?
S1: p > q
If p = 834
Then 2p = 1668 < 2000
If p = 418, q = 416
2 * 418 + 416 * 3.5, which will be greater than 2000
Insufficient
S2: q = 100
100 * 3.5 + 734 * 2 < 2000
If q = 834
834 * 3.5 > 2000
Combining both
Still insufficient

Correct option: E

Approach Solution (3):

p + q = 834
we need to know whether 2p + 3.5q > 2,000
(1) During the month, more units of P than units of Q were sold.
p > q
2p + 3.5q > 5.5q
But we do not know the value of q
Insufficient
(2) During the month, at least 100 units of Q were sold.
q >= 100, p <= 734
=> 2p + 3.5q >= 2p + 350
Insufficient
(1) + (2): p > 834/2 = 417
2p + 3.5q >= 2p + 350 > 834 + 350
Do not know the value of 2p + 3.5q
Insufficient

Correct option: E

“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 835 units of these products. Was the total profit on these items more than $2,000?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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