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Last year Luis invested x dollars for one year, half at 8

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Last year Luis invested x dollars for one year, half at 8 [#permalink] New post 03 Aug 2009, 01:00
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Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged, what fraction of the x dollars must he reinvest at the 12 percent rate so that the total interest earned from the x dollars will be the
same for both years ?

(1) The lower rate is now 6 percent.
(2) The total amount of interest earned from the two investments last year was $3,000.

[Reveal] Spoiler:
OA is A, I think it should be C
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Re: I think OA is wrong.. ! need help ! [#permalink] New post 03 Aug 2009, 01:11
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I think OA is correct.

half at 8% and half at 12% means 10% for x.
if we have 6% and 12% and still want to get 10% we need (my fast approach):
6 <--4-->10<--2-->12 or 4/(4+2)=2/3 invest at 12%.

It is a typical DS C-trap for % and means: often we don't need to know absolute value. So, if you are solving % problem and see absolute value only in options - be careful.
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Re: I think OA is wrong.. ! need help ! [#permalink] New post 03 Aug 2009, 01:22
walker wrote:
I think OA is correct.

half at 8% and half at 12% means 10% for x.
if we have 6% and 12% and still want to get 10% we need (my fast approach):
6 <--4-->10<--2-->12 or 4/(4+2)=2/3 invest at 12%.

It is a typical DS C-trap for % and means: often we don't need to know absolute value. So, if you are solving % problem and see absolute value only in options - be careful.


Thanks walker ... ! you made it easier and the fast approach is nice.. !
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Re: I think OA is wrong.. ! need help ! [#permalink] New post 03 Aug 2009, 16:58
statement 1 is sufficient since the question asks for the fraction, not the actual amount...via statement 1, you'll get 1/6...to move over to 12% from 6%
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Re: I think OA is wrong.. ! need help ! [#permalink] New post 05 Aug 2009, 06:52
statement 1 is sufficient.
we need only the ratio, not the actual amount.
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Re: I think OA is wrong.. ! need help ! [#permalink] New post 05 Aug 2009, 08:24
it will be easier to solve it with mixture and alligation approach...

given
calculate the total rate of interest ...u will see that it is x/10 hence resulting mixture will have 10% rate
mixture 1 (x/2 @ 8% ) ---->> ( total interest x @ 10%) <<---- mixture 2 ( x/2 @ 12%)
also ratio is given of split of total money x as 1:1

Statement (1) lower rate is 6%, hence a:b can be worked out ; which is nothing but our ans

mixture 1 (a @ 6% ) ---->> ( total interest x @ 10%) <<---- mixture 2 ( b @ 12%)

Statement (2) The total amount of interest $ 3000 hence total amount is $ 30,000 (10% interest rate resulted ...refer given) ...

mixture 1 (a @ z% ) ---->> ( total interest x @ 10% = $ 3000) <<---- mixture 2 ( b @ 12%)

this only results in (12%-10%) / (10%-z%) = a/b ..... 2/(10-z) = a/b....after using ratio properties also it is insufficient to ans.....

Hence OA A

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Re: I think OA is wrong.. ! need help !   [#permalink] 05 Aug 2009, 08:24
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