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A company makes and sells two products, \(P\) and \(Q.\) The costs per unit of making and selling \(P\) and \(Q\) are

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A company makes and sells two products, \(P\) and \(Q.\) The costs per unit of making and selling \(P\) and \(Q\) are

by Gmat_mission » Fri Jan 08, 2021 2:06 am

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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 \(\$2,000?\)

(1) During the month, more units of \(P\) than units of \(Q\) were sold.
(2) During the month, at least \(100\) units of \(Q\) were sold.

Answer: E

Source: Official Guide
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Source: — Data Sufficiency |
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Re: A company makes and sells two products, \(P\) and \(Q.\) The costs per unit of making and selling \(P\) and \(Q\) ar

by deloitte247 » Sun Jan 17, 2021 7:05 am

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Profit = cost price - selling price
Profit of P = $10 - $8 = $2
Profit of Q = $13 - $9.5 = $3.5
In 1 month, the company sold a total of 834 units of products P and Q.
So, P + Q = 834 and
P = 834 - Q
This will be 2P = 2 (834 - Q) and 2P = 1668 - 2Q

Target question: Was the total profit on these items more than $2000?
i.e 2P + 35Q > 2000?
Since 2P = 1668 - 2Q, the target question can be replaced to =>
1668 - 2Q + 3.5Q > 2000
-2Q + 3.5Q > 2000 - 1668
1.5Q > 332
Is Q > 221.3?

Statement 1: During the month, more units of P than units of Q were sold.
i.e P > Q
If P sold 700 units, then Q sold = 834 - 700 = 134 units and it is < 221.3.
If P sold 500 units, then Q = 834 - 500 = 334 units and it is > 221.3.
Since the answer is not definite, statement 1 is NOT SUFFICIENT.

Statement 2: During the month, at least 100 units of Q were sold.
i.e Q > 0
if P sold 100 units, then Q sold 154 and Q < 221.3.
But if P sold 500 units, then Q sold 334 and Q > 221.3.
Statement 2 is NOT SUFFICIENT

Combining both statements
There is no new information from both statements, so when combined together, they cannot be SUFFICIENT.

Answer = option E
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