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If x dollars are invested at 12 percent for one year and y dollars are

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If x dollars are invested at 12 percent for one year and y dollars are  [#permalink]

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New post 31 Mar 2019, 08:21
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If x dollars are invested at 12 percent for one year and y dollars are invested at 8 percent for one year, the annual income from the 8 percent investment will exceed the annual income from the 12 percent investment by $64. If $5,000 is the total amount invested between x and y, how much is invested at 12 percent?

A. $1,680
B. $1,997
C. $3,003
D. $3,320
E. $3,500

Source: McGraw-Hill's GMAT

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Re: If x dollars are invested at 12 percent for one year and y dollars are  [#permalink]

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New post 31 Mar 2019, 09:15
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You could guess A almost instantly here and be nearly sure you're right -- to make more money at 8% than at 12%, you'll need to invest a lot more at 8%, so the answer, the investment at 12%, needs to be far less than half of the total, so much less than $2500. So only A and B have any chance to be right, and for the difference to work out to an exact integer, $64, there is no chance the answer could be something weird like $1997.

But we can solve algebraically. If $x is invested at 12%, we make 0.12x on that investment. The rest, 5000-x, is invested at 8%, so we make (0.08)(5000-x) on that. The difference in those two quantities is $64, so we have:

0.08(5000 - x) - 0.12x = 64
400 - 0.08x - 0.12x = 64
336 = 0.2x
1680 = x
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Re: If x dollars are invested at 12 percent for one year and y dollars are  [#permalink]

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New post 31 Mar 2019, 10:15
SajjadAhmad wrote:
If x dollars are invested at 12 percent for one year and y dollars are invested at 8 percent for one year, the annual income from the 8 percent investment will exceed the annual income from the 12 percent investment by $64. If $5,000 is the total amount invested between x and y, how much is invested at 12 percent?

A. $1,680
B. $1,997
C. $3,003
D. $3,320
E. $3,500

Source: McGraw-Hill's GMAT

solve as per given info.

0.08(5000 - x) - 0.12x = 64
400 - 0.08x - 0.12x = 64
336 = 0.2x
1680 = x
IMO A
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Re: If x dollars are invested at 12 percent for one year and y dollars are   [#permalink] 31 Mar 2019, 10:15
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