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A total of $60,000 was invested for one year. Part of this

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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 27 Oct 2016, 08:08
RadhaKrishnan wrote:
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

(1) x = 3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.


Let the amounts be A and B.
Stem:
A + B = 60,000
Ax + By = 4,080

We have 4 variables, so we need 4 different equations.

Statement 1, x = 3y/4, gives us the relation between x and y but not x or y themselves

Statement 2, A=3B/2 , in combination with A + B = 60,000, gives us A and B but not x or y

With statements 1 and 2, we have the 4 equations needed.

Answer C
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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 27 Oct 2016, 09:35
VeritasPrepKarishma - I was trying to use weighted average with statement 1, can you pls help.

We are given that x/y = 3/4 and we can calculate the overall rate by using the 60,000 and the interest earned 4,080. using this won't we be able to get the ratio in which 60,000 would be invested at X and Y%?

Won't we enough data with equation 1 itself to solve it for X%?

TIA
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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 18 Nov 2016, 20:29
RadhaKrishnan wrote:
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

(1) x = 3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.



Answer: option C

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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 26 Apr 2017, 01:57
RadhaKrishnan wrote:
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

(1) x = 3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.



In most DS questions realising that the statements together or individually would lead to the answer is enough and not solving them to the end would save a lot of precious time as average time taken by PS questions are much more.

Here, you can start off with statement B and you can figure out the both the parts in which amount was divided. From there on, suing statement 1 you can either substitute the value of x for or vice versa. That will get you the answer without going through the complex method of solving the problem. If you're still not too sure, you can go ahead and solve the entire problem to be extremely sure.

All the best.
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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 30 Apr 2017, 05:03
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

(1) x = 3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

My 2 cents.
For this question, I think for non-native speaker as I am, it is important to realize that statement 2 is talking about the amount of x and y.
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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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gauravk wrote:
VeritasPrepKarishma - I was trying to use weighted average with statement 1, can you pls help.

We are given that x/y = 3/4 and we can calculate the overall rate by using the 60,000 and the interest earned 4,080. using this won't we be able to get the ratio in which 60,000 would be invested at X and Y%?

Won't we enough data with equation 1 itself to solve it for X%?

TIA


Using weighted averages,

4080/60,000 = 6.8%

Using stmnt 1:
w1/w2 = (4x/3 - 6.8)/(6.8 - x)
Now here is the problem: We don't know w1/w2 using stmnt 1 alone. So we cannot calculate the value of x.

Using stmnt 2, we get the value of w1/w2 which is 3/2. But here we don't have the ratio of x and y.

So you need both statements to get

3/2 = (4x/3 - 6.8)/(6.8 - x)

And now you can get a unique value of x.

Answer (C)
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Re: A total of $60,000 was invested for one year. Part of this [#permalink]

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New post 29 Aug 2017, 19:00
The whole trick is you set "a" amount and "60000-a" amount for X% and Y%.
Re: A total of $60,000 was invested for one year. Part of this   [#permalink] 29 Aug 2017, 19:00

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