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

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.

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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St 1 and 2 alone are insuff as both of them result into a linear equation with two variables.

Since these are linear equations in two variables together we can solve for x.

Hence correct ans is C.
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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
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You would still not know the amount invested at x% and the amount invested at y%.

If interest earned is 2448 at x%, what is the amount on which this interest is earned?
You could earn 2448 interest at 10% on 24480.
or you could earn 2448 interest at 5% on 48960.
etc.
x would be different in each case.
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here are my two cents for this question



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'


Hence Answer C

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