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The value of a rare baseball card A appreciated by 20 percent over a

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The value of a rare baseball card A appreciated by 20 percent over a  [#permalink]

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New post 22 Feb 2016, 04:36
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The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plummeted by 50 percent. Over the same total time period, the value of another card B increased by 100%. At the end of ten years, the reduced value of A was what percent of the increased value of B?

(1) Card A's initial value was $1000.
(2) The initial value of A was four times that of B.

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The value of a rare baseball card A appreciated by 20 percent over a  [#permalink]

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New post 22 Feb 2016, 05:18
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Let the initial value of a rare baseball card A = x
Over first 5 years , value of card A = 1.2 x
Over next 5 years , value of card A = (50/100 ) * 1.2 x = .6x

Let initial value of card B= y
Over the period of 10 years , value of card B = y + y = 2y

(1) Card A's initial value was $1000.
x= 1000$
After 10 years , value of card A = .6* 1000 = 600 $
However , we have no information on the increased value of B .
Not sufficient

(2) The initial value of A was four times that of B.
x=4y
Reduced value of card A after 10 years = .6x
Increased value of card B after 10 years = 2y = x/2

(Reduced value of A/Increased value of B)*100%
= (.6x / (x/2)) * 100%
=120%
Sufficient

Answer B
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Re: The value of a rare baseball card A appreciated by 20 percent over a  [#permalink]

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New post 22 Feb 2016, 19:10
The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plummeted by 50 percent. Over the same total time period, the value of another card B increased by 100%. At the end of ten years, the reduced value of A was what percent of the increased value of B?

after 10 years value of card A is .60A
value of card B is 2B
.6A/2B=?

(1) Card A's initial value was $1000.
no info on card B
Insufficient

(2) The initial value of A was four times that of B.
A=4B
.6*4B / 2B
Sufficient

Answer: B
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Re: The value of a rare baseball card A appreciated by 20 percent over a  [#permalink]

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New post 22 Feb 2016, 22:02
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plummeted by 50 percent. Over the same total time period, the value of another card B increased by 100%. At the end of ten years, the reduced value of A was what percent of the increased value of B?

(1) Card A's initial value was $1000.
(2) The initial value of A was four times that of B.


In general, if one con is number and the other con is ratio, it is most likely that ratio is an answer.
When you modify the original condition and the question, A-->1.2A-->1.2A*0.5=0.6A and B-->2B. Since the question is the value of 0.6A was what per cent of the value of 2B, the relation between A and B should be given.
In 2), A=4B is given, which is sufficient.
Therefore, the answer is B.


 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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New post 25 Aug 2018, 13:11
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