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GGUY
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I built two 2 variables formulas, which took me 4 min (!) to 17 Jan 2008, 06:01
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I built two 2 variables formulas, which took me 4 min (!) to solve. any thought on how to solve it faster?

If x dollars is invested at 10 percent for one year and
y dollars is invested at 8 percent for one year, the
annual income from the 10 percent investment will
exceed the annual income from the 8 percent
investment by $56. If $2,000 is the total amount
invested, how much is invested at 8 percent?

(A) $280
(B) $800
(C) $892
(D) $1,108
(E) $1,200



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I built two 2 variables formulas, which took me 4 min (!) to 17 Jan 2008, 06:16
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GGUY
I built two 2 variables formulas, which took me 4 min (!) to solve. any thought on how to solve it faster?

If x dollars is invested at 10 percent for one year and
y dollars is invested at 8 percent for one year, the
annual income from the 10 percent investment will
exceed the annual income from the 8 percent
investment by $56. If $2,000 is the total amount
invested, how much is invested at 8 percent?

(A) $280
(B) $800
(C) $892
(D) $1,108
(E) $1,200
Show more

The test makers like to give answer pairs that catch up people who aren't paying attention. As you can see and . They do this to catch people who aren't paying attention to what is being asked. This is usually a sign that the answer is in one of these pairs. If you don't believe it though, I think it's safe to say that 8% of 280 is a lot smaller than $56 less than 10% of $1720. Eliminate choice A.

As we can see, the 8% rate will come from a smaller investment. For the two rates to be earned on the same amount and for there to be a $56 disparity they would have to be invested in (56*50 = 2800) $2800. Since we're working with numbers significantly smaller than this we know that the 8% is being earned on a smaller amount. This narrows it down to $800 and $892. Eliminate D and E. I do the math on the easiest of the two remaining choices, and if it doesn't work choose the other choice.







and we got lucky right off the bat. Make sure you're answering the right question (how much is invested at 8%)

Answer B
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I built two 2 variables formulas, which took me 4 min (!) to 17 Jan 2008, 18:53
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if i wanted to do this the algebraic way, what equation could i write to express the difference in the incomes ?

is it 1.1x = 1.08y + 56
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I built two 2 variables formulas, which took me 4 min (!) to 17 Jan 2008, 19:33
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GGUY
I built two 2 variables formulas, which took me 4 min (!) to solve. any thought on how to solve it faster?

If x dollars is invested at 10 percent for one year and
y dollars is invested at 8 percent for one year, the
annual income from the 10 percent investment will
exceed the annual income from the 8 percent
investment by $56. If $2,000 is the total amount
invested, how much is invested at 8 percent?

(A) $280
(B) $800
(C) $892
(D) $1,108
(E) $1,200
Show more


Ix=X1/10t
Iy=Y2/25t

Ix=Iy+56 --

Iy+56=X1/10
Iy=Y2/25

X+Y=2000

X=2000-Y

Y2/25+56=(2000-Y)/10 ---> 4Y/5+560=2000-Y 9Y/5=1440 Y=800

B
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I built two 2 variables formulas, which took me 4 min (!) to 17 Jan 2008, 21:21
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eschn3am
GGUY
I built two 2 variables formulas, which took me 4 min (!) to solve. any thought on how to solve it faster?

If x dollars is invested at 10 percent for one year and
y dollars is invested at 8 percent for one year, the
annual income from the 10 percent investment will
exceed the annual income from the 8 percent
investment by $56. If $2,000 is the total amount
invested, how much is invested at 8 percent?

(A) $280
(B) $800
(C) $892
(D) $1,108
(E) $1,200

The test makers like to give answer pairs that catch up people who aren't paying attention. As you can see and . They do this to catch people who aren't paying attention to what is being asked. This is usually a sign that the answer is in one of these pairs. If you don't believe it though, I think it's safe to say that 8% of 280 is a lot smaller than $56 less than 10% of $1720. Eliminate choice A.

As we can see, the 8% rate will come from a smaller investment. For the two rates to be earned on the same amount and for there to be a $56 disparity they would have to be invested in (56*50 = 2800) $2800. Since we're working with numbers significantly smaller than this we know that the 8% is being earned on a smaller amount. This narrows it down to $800 and $892. Eliminate D and E. I do the math on the easiest of the two remaining choices, and if it doesn't work choose the other choice.







and we got lucky right off the bat. Make sure you're answering the right question (how much is invested at 8%)

Answer B
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eschn3am, I set up an equation and get the result in 2 minutes and 26 seconds. I like this approach. The expertise in recognization is very important. And "As we can see, the 8% rate will come from a smaller investment. For the two rates to be earned on the same amount and for there to be a $56 disparity they would have to be invested in (56*50 = 2800) $2800" is not clear for me.
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I built two 2 variables formulas, which took me 4 min (!) to 18 Jan 2008, 05:42
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Quote:
"As we can see, the 8% rate will come from a smaller investment. For the two rates to be earned on the same amount and for there to be a $56 disparity they would have to be invested in (56*50 = 2800) $2800" is not clear for me.

Show more

Let's pretend that the 8% and 10% are being earned on the same amount. Now let's pretend the difference in the amounts earned is $2. The 2% (10%-8%) is equal to $2.

2% = $2
Multiply each side by 50
100% = $100

so if the amounts of money were equal and the difference was $2, then the two accounts would each have $100 in them.

However, we have 8% and 10% (so we still have our 2%), but we have $56

2% = $56 or .02 = 56
Multiply each side by 50
100% = $2800

so if the amounts were invested equally, to earn $56 more they would have to be earning interest on $2800.

Now, we know that this is impossible because the amounts total to be $2000. We know they can't be investing the same amount because $1000 and $1000 is less than $2800 so the difference will be way less than $56. The only way for this to work out is if the 10% is being earned on a larger amount than the 8%. This is how I narrow it down to just 2 choices and come to the answer quickly.
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I built two 2 variables formulas, which took me 4 min (!) to 18 Jan 2008, 07:49
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x - amount invested at 10%, y - invested at 8%

x + y = 2,000
0.1*x-0.08*y = 56 -> x - 0.8*y = 560. Now we subtract the second equation from the first one and get
1.8*y = (2000-560) -> y = 800

B is the answer.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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