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

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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] ### Show Tags 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 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 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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The whole trick is you set "a" amount and "60000-a" amount for X% and Y%.
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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 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 Scott@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Senior Manager  P Status: Gathering chakra Joined: 05 Feb 2018 Posts: 443 Re: A total of$60,000 was invested for one year. Part of this  [#permalink]

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I mistakenly read (2) as saying "the amount of interest earned at x" rather than "the amount that earned interest." If it was said in the former way (2) would be sufficient on its own, right? You could find the value of each out of 4080, so you could also determine x% and y% from just (2). Would the GMAT do something tricky like this?

4080/5 = 816
So 2448 at x and 1632 at y.
2448/4080 = .6 and 1632/4080 = .4
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Thanks, now that I reread your posts and wrote it all out on paper it's very clear.

I wasn't writing things down previously, so in my head I was confusing the ratio of $Amt earned from Amt1 & Amt2 with the ratio of %interest. Regardless of how the might've question put it, both the total amount and the subsequent interest is divided in a ratio of 3:2 (36k to 24k or 2448 to 1632), this is the weight 1 & weight 2. But this says nothing about the ratio of the x & y%. As you succinctly put it we can accrue the same interest from Amt1 & Amt2 in different amounts based on x & y% As always thanks for all your amazing blog posts... fundamentally understanding mixtures/weighted average/statistics concepts instead of just applying formulas has been my Achilles heel... it's much worse than combinatorics and probability. Senior Manager  P Joined: 10 Apr 2018 Posts: 269 Location: United States (NC) A total of$60,000 was invested for one year. Part of this  [#permalink]

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here are my two cents for this question

Attachment: Sample.png [ 9.88 KiB | Viewed 65 times ]

Avg interest is $$\frac{4080}{60,000}$$ =6.8 ( hidden information in Stem)

Using concept of allegations

We have a information that is represented by figure 1 ( From Question Stem)
we can see that we need values of X or Y and 'a' or 'b'. IN this regard if we have any relation in term of X and Y and some relation between 'a' and 'b' .

Now from statement 1:
we have a relation between X and Y but we don't have any relation or values of 'a' and 'b'.

Now from statement 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." This information gives a relation between 'a' and 'b'
But in absence of any information regarding "X" and "Y" we cannot find out the value of "X"

Combining both statements we do have information of "x" and "y" and also information about 'a' and 'b'

Avg interest is $$\frac{4080}{60,000}$$ =6.8 ( hidden information in Stem)
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Originally posted by Probus on 12 Jan 2020, 14:10.
Last edited by Probus on 13 Jan 2020, 19:44, edited 1 time in total.
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Re: A total of $60,000 was invested for one year. Part of this [#permalink] ### Show Tags 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 amount that earned interest at x% be A and the remaining amount that earned y% be (60,000- A).
So, A * .x + (60,000 -A) * .y = 4,080
Here we have 3 unknowns and one equation. So, we may need two more equations.

1) From this we can get the relationship between x and y. But not the single value of x. insufficient
2) It says A = 36,000 but no more information. not sufficient by itself.
From 1 and 2, we get 2 different equations, which is enough to solve the value of x. Re: A total of $60,000 was invested for one year. Part of this [#permalink] 12 Jan 2020, 15:54 Go to page Previous 1 2 [ 35 posts ] Display posts from previous: Sort by # A total of$60,000 was invested for one year. Part of this  