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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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

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: Beat The GMAT — Data Sufficiency | Fri Jan 08, 2021 2:06 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

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