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It takes 3 tons of copper ore and 5 tons of iron ore to make o

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It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 09 Aug 2015, 05:38
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It takes 3 tons of copper ore and 5 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?

(A) 18
(B) 18 3/4
(C) 20
(D) 30
(E) 50
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 09 Aug 2015, 08:29
3c + 5i = a
60c + 90i = ?

20(3c + 5i) = 60c + 100i = 20a, so the answer has to be less than 20 since we are dealing with 90i.

But, 18(3c + 5i) = 54c + 90i = 18a, here we get 54c < 60c. So answer must be 18 3/4 (B).
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 10 Aug 2015, 03:04
FireStorm wrote:
3c + 5i = a
60c + 90i = ?

20(3c + 5i) = 60c + 100i = 20a, so the answer has to be less than 20 since we are dealing with 90i.

But, 18(3c + 5i) = 54c + 90i = 18a, here we get 54c < 60c. So answer must be 18 3/4 (B).


why not A
if you produce 18 3/4 the copper is not enough.
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 10 Aug 2015, 03:28
IMO, this is a max/min problem, where the amount of alloy A is limited to how much material we have. Since we need more iron ore to make alloy A than we do from copper ore, iron ore is limiting factor, and therefore, we have enough iron ore only to make 18 tons of alloy A. Answer A.
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 11 Aug 2015, 03:33
applebus wrote:
FireStorm wrote:
3c + 5i = a
60c + 90i = ?

20(3c + 5i) = 60c + 100i = 20a, so the answer has to be less than 20 since we are dealing with 90i.

But, 18(3c + 5i) = 54c + 90i = 18a, here we get 54c < 60c. So answer must be 18 3/4 (B).


why not A
if you produce 18 3/4 the copper is not enough.


Yes, none of the given options works perfectly. But the answer must be between 18 and 20, so I chose 18 3/4, although it doesn't fit all too well.
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 11 Aug 2015, 06:08
It's an alloy, so you need both metals to make it. If you had 150 tons of copper ore you would not be able to make any amount of the alloy, you would just have copper ore. Therefore, the answer is A.
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 11 Aug 2015, 21:44
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Yes, you need copper ore:iron ore in the ratio 3:5. Total 8 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/3 = 20 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/5 = 18 tons of alloy A.

Since iron ore is available for only 18 tons of alloy A, you can make only 18 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.

Answer must be 18.

(A)

Note: This reminds me of our maximum power of 6 in 40! kind of questions. We have many 2s but fewer 3s. We can make only as many 6s as the number of 3s we have. The leftover 2s alone cannot make a 6. Makes sense?
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o  [#permalink]

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New post 03 Jul 2018, 04:29
VeritasPrepKarishma wrote:
Yes, you need copper ore:iron ore in the ratio 3:5. Total 8 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/3 = 20 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/5 = 18 tons of alloy A.

Since iron ore is available for only 18 tons of alloy A, you can make only 18 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.

Answer must be 18.

(A)

Note: This reminds me of our maximum power of 6 in 40! kind of questions. We have many 2s but fewer 3s. We can make only as many 6s as the number of 3s we have. The leftover 2s alone cannot make a 6. Makes sense?


Struggled with this for almost 15 minutes , I also tried to take the average of 18 tons of alloy and 20 tons of alloy . When no answer matched I thought I was doing something wrong .
Then I finally scrolled down and behold , I saw Karishma' s post , then a bulb lit up and every thing became clear . True to her name Karishma is indeed a magician !
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Re: It takes 3 tons of copper ore and 5 tons of iron ore to make o &nbs [#permalink] 03 Jul 2018, 04:29
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