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27 Oct 2016, 08:08
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 _________________ Clipper Ledgard GMAT Coach Manager Joined: 29 Aug 2008 Posts: 110 Re: A total of$60,000 was invested for one year. Part of this  [#permalink]

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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%?

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

Check solution as attached
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Re: A total of $60,000 was invested for one year. Part of this [#permalink] ### Show Tags 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] ### Show Tags 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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29 Aug 2017, 19:00
The whole trick is you set "a" amount and "60000-a" amount for X% and Y%.
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08 Nov 2018, 22:02
OA:C

Amount invested with $$x$$ % interest rate = $$$z$$ Amount invested with $$y$$ % interest rate =$ $$60000-z$$

$$\frac{x}{100}*z*1+\frac{y}{100}*(60000-z)*1 =4080$$....(1)

We have to find the value of $$x$$

(1) $$x = \frac{{3y}}{4} \quad$$ ; Putting $$\quad y=\frac{4x}{3}$$ in (1) , we get

$$\frac{x}{100}*z*1+\frac{{4x}}{{3*100}}*(60000-z)*1 =4080$$

We still do not know the value of $$z$$, So we cannot find out the value of $$x$$.

Statement (1) alone is insufficient.

(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 $$2$$.

$$\frac{z}{60000-z}=\frac{3}{2}$$

$$z=36000$$ $$$60000-z = 24000$$$

$$\frac{x}{100}*36000*1+\frac{y}{100}*24000*1 =4080$$

We still do not know the value of $$y$$ or relation of $$y$$ with $$x$$, So we cannot find out the value of $$x$$.

Statement (2) alone is insufficient.

Combining (1) and (2), we get

$$\frac{x}{100}*36000*1+\frac{{4x}}{{3*100}}*24000*1 =4080$$

Using this equation, We can get the value of $$x$$.
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Re: A total of $60,000 was invested for one year. Part of this [#permalink] ### Show Tags 09 Nov 2018, 12:30 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.

We are given that $60,000 was invested for 1 year. We are also given that part of the investment earned x percent simple annual interest and the rest earned y percent simple annual interest. We are also given that the total interest earned was$4,080. Let’s start by defining a variable.

b = the amount that earned x percent simple interest

Using variable b, we can also say:

60,000 – b = the amount that earned y percent simple annual interest

Since we know that the total interest earned was $4,080, we can create the following equation: b(x/100) + (60,000 – b)(y/100) = 4,080 Note that in the equation above, we express "x percent" as x/100 and "y percent" as y/100 in the same way that we would express, say, 24 percent as 24/100. Statement One Alone: x = 3y/4 Although we have an equation with x and y, we still need a third equation to be able to determine the value of x because our equation from the given information has three variables. Statement one alone is not sufficient to answer the question. Statement Two Alone: 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. From our given information we know that b is the amount that earned interest at the rate of x percent per year and that 60,000 – b is the amount that earned interest at the rate of y percent per year. Thus, we can create the following equation: b/(60,000 – b) = 3/2 Without a third equation, statement two alone is not sufficient to determine the value of x. Statements One and Two Together: From the given information and statements one and two we have the following 3 equations: 1) b(x/100) + (60,000 – b)(y/100) = 4,080 2) x = 3y/4 3) b/(60,000 – b) = 3/2 Since we have 3 independent equations with variables x, y, and b, we are able to determine the value of x. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: A total of$60,000 was invested for one year. Part of this &nbs [#permalink] 09 Nov 2018, 12:30

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