An hairstylist gave a haircut to 80 % of her clients and shaved 40%

Question

An hairstylist gave a haircut to 80% of her clients and shaved 40% of her clients. She charged $5 for a haircut and $7 for a shave. If 20% of clients who opted for a shave also had a hair-cut, what was Monika’s earnings if she had 75 customers?

A. 560
B. 510
C. 460
D. 410
E. 350

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ManifestDreamMBA · Answer

Customers = 75
Haircut customers = 4/5 * 75 = 60
Hair cut earning = 60*5 = 300

Shave customers = 2/5 * 75 = 30
Shave earnings = 30*7 = 210

Total earnings = 510

PS: I am not sure why overlap is given. Unlike sets where we are counting distinct entities, double counting here is required to find the earnings. It would have been different if the combined rate was discounted or something

kingbucky · Answer

80% of clients get a haircut at $5, 40% get a shave at $7, and we need total earnings. The 20% overlap of shave clients getting haircuts is noted but seems unnecessary.

We’ll compute the number of haircuts and shaves, their costs, and sum the earnings, as shown in the table below.

Service  
  Number of clients who availed the service  
  Revenue  
 
    Haircut   
   80% of 75 =  0.8 	imes 75 = 60  clients   
    60 	imes 5 = 300  dollars   
 
    Shave   
   40% of 75 =  0.4 	imes 75 = 30  clients   
    30 	imes 7 = 210  dollars

Total revenue is the sum of haircut and shave earnings:   
 	ext{Total} = 300 + 210 = 510

The 20% of shave clients who also got haircuts is extraneous, as we directly know 60 haircuts and 30 shaves occurred, and earnings are based on services provided, not overlaps.

Thus, Monika’s earnings are $510.

Answer: B

Pj20 · Answer

Id still like to understand why the number of clients become 30+60 when her no of customers 75?

Krunaal · Answer

80% of 75 = 60 get a Haircut

40% of 75 = 30 get a Shave

But there are some who do both! And those are 20% of 75 = 15 who opted for a shave as well as haircut

So from overlapping sets formula:  Total - Neither = Haircut + Shave - Both  =>  75 - 0 = 60 + 30 - 15  =>  75 = 75  therefore LHS = RHS. Hope it clears your doubt.

PS.
I feel the wording is a little ambiguous here  "   If    20% of clients who opted for a shave    also had a hair-cut"  could translate to 20% of 30 (the ones who opted for a shave) = 6 also had a haircut, but ofc the intent here is 20% of total customers i.e. 20% of 75 opted for both. Or maybe it's just me reading it wrong.

An hairstylist gave a haircut to 80 % of her clients and shaved 40%

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Service	Number of clients who availed the service	Revenue
Haircut	80% of 75 = \(0.8 \times 75 = 60\) clients	\(60 \times 5 = 300\) dollars
Shave	40% of 75 = \(0.4 \times 75 = 30\) clients	\(30 \times 7 = 210\) dollars

GMAT Problem Solving (PS) Questions

An hairstylist gave a haircut to 80 % of her clients and shaved 40%

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