A company makes a profit of 6 percent on its first

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A company makes a profit of 6 percent on its first

by BTGmoderatorLU » Wed Jun 06, 2018 2:53 pm

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A company makes a profit of 6 percent on its first $1,000 of sales each day, and 5 percent on all sales in excess of $1,000 for that day. How many dollars in profit will the company make on a day when sales are S dollars if S is greater than 1,000?

A. 0.05S
B. 0.06S
C. 110
D. 10 + 0.05S
E. 60 + 0.05S

The OA is D.

We can just plug in some values to find out:

Say S = 1100
For the first 1000, profit is 6% i.e. $60
For the next 100, profit is 5% i.e. $5
Total profit is $65

Plug in 1100 in the options and you see that option D will give you 65.

Please, can anyone explain another way to solve this PS question? Thanks!

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Source: Beat The GMAT — Problem Solving | Wed Jun 06, 2018 2:53 pm

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Fri Jun 08, 2018 12:34 am

BTGmoderatorLU wrote:A company makes a profit of 6 percent on its first $1,000 of sales each day, and 5 percent on all sales in excess of $1,000 for that day. How many dollars in profit will the company make on a day when sales are S dollars if S is greater than 1,000?

A. 0.05S
B. 0.06S
C. 110
D. 10 + 0.05S
E. 60 + 0.05S

The OA is D.

Hello BTGmoderatorLU.

Let's see another way to solve it.

The sales of the company on a day are S > $1,000.

Then, for the first $1,000 the profit is equal to $$P_1=1,000\cdot6\%=1,000\cdot\frac{6}{100}=10\cdot6=60.$$ Thta is to say, for the first $1,000 the company makes a profit of $60.

Now, the amount of dollars in excess of $1,000 we can represent it by S-1,000. Therefore, the profit for the excess of $1,000 is equal to $$P_2=\left(S-1,000\right)\cdot5\%=\left(S-1,000\right)\cdot\frac{5}{100}=\left(S-1,000\right)\cdot\frac{1}{20}=\frac{1}{20}\cdot S-\frac{100}{2}=0.05\cdot S-50.$$ Finally, the company wil make in profit the following amount of dollars $$P_1+P_2=60+0.05\cdot S-50=10+0.05\cdot S$$ This implies thta the correct answer is the option D.

I hope it helps you.

Regards.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 08, 2018 10:23 am

BTGmoderatorLU wrote:A company makes a profit of 6 percent on its first $1,000 of sales each day, and 5 percent on all sales in excess of $1,000 for that day. How many dollars in profit will the company make on a day when sales are S dollars if S is greater than 1,000?

A. 0.05S
B. 0.06S
C. 110
D. 10 + 0.05S
E. 60 + 0.05S

We can create the expression for the total profit earned:

0.06(1000) + 0.05(S - 1000)

60 + 0.05S - 50

0.05S + 10

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]