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

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Math Expert
Joined: 02 Sep 2009
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Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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08 Jan 2018, 07:33
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Difficulty:

45% (medium)

Question Stats:

48% (01:14) correct 52% (01:45) wrong based on 31 sessions

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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. $$5,000 - 1,020a$$

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Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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Updated on: 23 Jan 2018, 04:50
1
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.
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Originally posted by mandeey on 08 Jan 2018, 09:05.
Last edited by mandeey on 23 Jan 2018, 04:50, edited 2 times in total.
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Posts: 58453
Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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08 Jan 2018, 09:11
mandeey wrote:
Selling price = 5000-2a
Cost price = 1000

Profit = S.P -C.P = 5000-2a-1000 = 4000-2a

Ans. 4000-2a

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

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Done. Thank you.
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Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 07:34
Bunuel wrote:
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

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$$^2$$

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

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Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 08:06
Bunuel wrote:
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

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
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Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 09:37
Bunuel wrote:
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

a identical rare coins or an identical rare coin or identical rare coins (without article) ?:)
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Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 10:36
1
dave13 wrote:
Bunuel wrote:
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

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

Hi dave13

$$a$$ is a variable here. Formatted the question.
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Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 11:00
IMO C.

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

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

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Posts: 4
Re: Adam originally acquired a identical rare coins for 1,000 dollars each  [#permalink]

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22 Jan 2018, 12:05
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.
Re: Adam originally acquired a identical rare coins for 1,000 dollars each   [#permalink] 22 Jan 2018, 12:05
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