Adam originally acquired a identical rare coins for 1,000 dollars each

Question

Adam originally acquired  a  identical rare coins for  1,000  dollars each. Suppose the price at which he sells each coin is  5000 – 20a , what is his total profit?

A.  4,000 – 19a 
B.  4,000 – 20a^2 
C.  4,000a – 20a^2 
D.  4,000 - 20a 
E.  5,000 - 1,020a

mandeey · Answer

Selling price = 5000-20a
Cost price = 1000

Profit = S.P -C.P = 5000-20a-1000 = 4000-20a

profit of 'a' items = (4000-20a)*a = 4000a-20 a^2

Bunuel  Please correct options B or D, both are same.

Bunuel · Answer

_______________
Done. Thank you.

generis · Answer

The twist in this problem: quantity  a  just happens to be part of calculating the sell price. Sell price still has to be multiplied by quantity  a  to get total revenue.

Algebra 
Total cost: (cost per coin)*(# of coins) = 1,000a

Total revenue: (price per coin)*(# of coins)
(5,000 - 20a)*(a) = 5,000a - 20a ^2

Total profit: Total revenue - total cost
(5,000a - 20a ^2 ) - 1,000a
5,000a - 20a ^2  - 1,000a
4,000a - 20a ^2

Answer C

Assign values

This question is not very amenable to assigning values. If you use a = 1, e.g., answers B, C, D, and E will work.

Nonetheless, if you are stuck on the algebra, use a round number. (20a is a clue. A round number there is good, as is a round number when 5,000 - 20a is multiplied by "a.")

Let a = 10

Total cost of 10 coins, in $, at 1,000 per coin = 10,000

Sell price, in $: 
5,000 - (20)(10) = 5,000 - 200 = 4,800 per coin

Total revenue: (4,800)*10 = 48,000

Profit = Total revenue - total cost
48,000 - 10,000 = 38,000

With a = 10, find the answer choice that yields 38,000

Eliminate A, B, D, and E
Their starting number (4,000 or 5,000) is much less than $38,000, let alone after some amount has been subtracted.

By process of elimination, the answer is C.
Check: 4,000a – 20a ^2 
(4,000)(10) - (20)(10 ^2 )
40,000 - (20)(100)
40,000 - 2,000 = 38,000 MATCH

Answer C

anugrahs · Answer

IMO: C I got confused with 'a' in the initial sentence

Anyways, Cost Price of 1 coin = 1000 Selling Price of 1 coin = 5000 - 20a Profit on 1 coin = SP - CP = (5000 - 20a) - 1000 = 4000 - 20a Now he sold 'a' such coins Thus total profit = a * (4000 - 20a) = 4000a - 20 a^2 Thus option C

dave13 · Answer

a identical rare coin s  or an identical rare coin or identical rare coins (without article) ?:)

niks18 · Answer

Hi  dave13

a  is a variable here. Formatted the question.

prerakgoel03 · Answer

IMO C.

Profit on one coin(5000-20a-1000)=4000-20a

Now for a coins profit is a(4000-20a)=4000a-20a^2

Sent from my iPhone using GMAT Club Forum

adiitya · Answer

Profit = Money earned by selling - Money invested for purchasing
 = S.P*number of items - C.P*number of items
 = (5000-20a)*a - (1000)*a
 = 5000a-1000a-20a^2
 = 4000a - 20a^2

Hence C.

Adam originally acquired a identical rare coins for 1,000 dollars each

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Adam originally acquired a identical rare coins for 1,000 dollars each

Prep Toolkit

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