Weighted Average

[GMATMadeEasy]

Company X has three revenue streams generated from selling electical appliances. Revenue generated from
warrantee sales is 10% of the price at which an appliance is sold and revenue generated from nancing is
equal to 30% of the price at which an appliance is sold. If last year Company X sold 10,000 appliances,
15% of all sales were nanced, and 35% of all customers bought warrantees, resulting in 4.28 million dollars
in revenue, what was the average amount of revenue generated per appliance sold?
A. $407
B. $428
C. $456
D. $484
E. $512

Could someone suggest the best way to solve this problem .

[pesfunk]

What is the source of the question ?

I chose B. If we already know that 10,000 appliances were sold and a total of 4.28 million dollars was the revenue.
Well, in that case, I would straight away divide the revenue with the 10,000 and come to option B.

If B is not the option, probably the question has something missing.

Company X has three revenue streams generated from selling electical appliances. Revenue generated from
warrantee sales is 10% of the price at which an appliance is sold and revenue generated from nancing is
equal to 30% of the price at which an appliance is sold. If last year Company X sold 10,000 appliances,
15% of all sales were nanced, and 35% of all customers bought warrantees, resulting in 4.28 million dollars
in revenue, what was the average amount of revenue generated per appliance sold?
A. $407
B. $428
C. $456
D. $484
E. $512

Could someone suggest the best way to solve this problem .

[limestone]

In my understanding:

X sold 10,000 units and received 4.28 mil USD.
35% units sold got warranty.
15% of all sales were nanced.

My approach:

Price of each unit: 4,280,000/10,000 = 428
If all units got warranty, the average price would be : (100%+10%)*428
However, only 35% got warranty, then the average price would be: (100+10%*35%)* 428
= 428 + 428*3.5%
= about 428 + 15
= about 443
The sales of each units and warranty made up only 85% of total sales, then the average price must be:
443/ (85%) or
= 443*100/85
= 443* 1 + 443*15/85
= about 443 + 443*1/6
= about 443 + 74
= about 517
Hence Pick E. Bold phase represent for approximate number.


Another way is use formal approach:

Sales of 10,000 units = 4,280,000
Sales of 35% warranty = 4,280,000*35%*10% = 149800
Sales of warranty and 10,000 units = 4429800
Sales of warranty and 10,000 units made up only 85% total sales, then total sales must be:
4429800/85% = 5211529

Average price = 5211529/10000 = 521

Pick E, and I think E should be 521, instead of 512 as in the given information.


IMO: formal approach can not be applied within 2 minutes as it requires so many calculation. So use approximate number is recommended.