A salesman sold vacuum cleaners with a special 30-day...

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

A salesman sold vacuum cleaners with a special 30-day...

by BTGmoderatorLU » Sat Oct 28, 2017 8:34 am

A salesman sold vacuum cleaners with a special 30-day, money-back guarantee. He sold a total of T vacuum cleaners at a price of D each. Q of the vacuum cleaners were returned within 30 days, and the salesman returned the money to those people. Which of the following expressions represents the money the salesman got from actual sales (people that kept their vacuum cleaners) as a percentage of the total amount of money that he made before having to make refunds?

A) 100% Ã— TD/QD
B) 100% - Q/TD
C) (100% - (100QD))/TD
D) 100%(TD - QD)/TD
E) 100%(TD - QD)

The OA is D.

Can any expert assist me with this PS question, please? I need help to solve it. Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Oct 28, 2017 8:34 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Oct 28, 2017 1:42 pm

A salesman sold vacuum cleaners with a special 30-day, money-back guarantee. He sold a total of T vacuum cleaners at a price of D each. Q of the vacuum cleaners were returned within 30 days, and the salesman returned the money to those people. Which of the following expressions represents the money the salesman got from actual sales (people that kept their vacuum cleaners) as a percentage of the total amount of money that he made before having to make refunds?

A) 100% X TD/QD
B) 100% - Q/TD
C) (100% - (100QD))/TD
D) 100%(TD - QD)/TD
E) 100%(TD - QD)

The OA is D.

Hi LUANDATO,
Let's take a look at your question.

Total Vacuum clear sold = T
Cost of each Vacuum cleaner = D
Total Money made for selling T Vacuum cleaners = TD

Number of Vacuum cleaners returned = Q
Amount that salesman had to refund = (Number of Vacuum cleaners)(Cost of each Vacuum cleaner)
= QD

The amount that salesman is left with, after refunds = TD - QD
We are asked to write this remaining amount as a percent of the Total money made before the refunds.
Percent Amount = 100%[(Amount that salesman is left with, after refunds)/(Total Money Made)]
$$=100\%\frac{\left(TD-QD\right)}{TD}$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
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Our average student improves 98 points.

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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 » Tue Nov 12, 2019 7:16 pm

BTGmoderatorLU wrote:A salesman sold vacuum cleaners with a special 30-day, money-back guarantee. He sold a total of T vacuum cleaners at a price of D each. Q of the vacuum cleaners were returned within 30 days, and the salesman returned the money to those people. Which of the following expressions represents the money the salesman got from actual sales (people that kept their vacuum cleaners) as a percentage of the total amount of money that he made before having to make refunds?

A) 100% Ã— TD/QD
B) 100% - Q/TD
C) (100% - (100QD))/TD
D) 100%(TD - QD)/TD
E) 100%(TD - QD)

The OA is D.

Can any expert assist me with this PS question, please? I need help to solve it. Thanks.

We can let T = 4, D = 1, Q = 2.

Thus, the money originally made was 4.

After the returns, the money made was 2.

The money made from sales as a percentage of the money made prior to returns was:

2/4 = 50%

Looking at the answer choices, D gives us 50%:

100%(4 - 2)/4 = 2/4 = 1/2 = 50%.

Answer: D

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