For a shipment of n bottles of a certain product, a mail order firm ch

Question

For a shipment of n bottles of a certain product, a mail order firm charges a price of $40.00 per bottle, plus a shipping fee of 5 percent of the total price of the n bottles, plus a handling fee of $5.00 per shipment. What is the least value of n for which the total charge per bottle shipped is less than $42.50 ?

A) 26
B) 21
C) 18
D) 11
E) 6

A) 26
B) 21
C) 18
D) 11
E) 6

houston1980 · Accepted Answer

Logic can be used to know the right answer.

With 5% tax, the charge per bottle is $42 excluding shipping.

Shipping is $5 irrespective of the number of bottles..

The shipment charges for 10 bottles is 50 cent or $0.50 per bottle.
For 10 bottles, the total charge per bottle is $42.50.

For 11 bottles, the shipping charges per bottle is less than $0.50.

Therefore for 11 bottles and more, the total charges is less than $42.50 per bottle.

Therefore option  D  is the answer.

RiyazAhamed · Answer

Good question.

Let the number of bottles be N.

Total cost be: T =  40(N) + \frac{5}{100}*40(N) + 5

Asked for, when will  \frac{T}{N} < 42.5 ? or When will  T < 42.5N?

Equating the equations:

T < 42.5N? 
 40(N) + \frac{5}{100}*40(N) + 5 < 42.5N 
 42(N) + 5 < 42.5N 
 10 < N

The Answer is 11. D.

gmatophobia · Answer

Each bottle has a fixed price of $40, hence other chargers, which include a 5% shipping fee and the handling fee should be equal to $2.50.

Hence, we can translate the question as -

What is the least value of n for which the shipping fee and handling fee are less than $2.50

Shipping Fee per bottle =  5 % of  40

Handling Fee per bottle =  \frac{5}{n}

5 % of  40 + \frac{5}{n} < 2.50

2 + \frac{5}{n} < 2.50

n > 10

Hence, least number = 11

Option D

DanTheGMATMan · Answer

Set up the cost, and remember to divide by N because its the cost PER BOTTLE SHIPPED:
 https://www.youtube.com/watch?v=7PTyB3UH-7I

bumpbot · Answer

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For a shipment of n bottles of a certain product, a mail order firm ch

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For a shipment of n bottles of a certain product, a mail order firm ch

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