Saul invests an amount of dollars in investment A at i% simple annual interest, another amount in...

[BTGmoderatorLU]

Source: Manhattan Prep

Saul invests an amount of dollars in investment A at i% simple annual interest, another amount in investment B at j% simple annual interest, and a third amount in investment C at k% simple annual interest. If the percent interest rates i, j, and k are in a ratio of 3:2:4, what is the ratio of the average rate of interest on all three investments (taken together) to the interest rate on investment A?

1) The amounts Saul invested in investments A, B, and C are in a ratio of 1:4:5.

2) Saul’s three investments total $100,000, while the total amount of money he earns in interest in the first year is $18,600

The OA is A

[Jay@ManhattanReview]

Source: Manhattan Prep

Saul invests an amount of dollars in investment A at i% simple annual interest, another amount in investment B at j% simple annual interest, and a third amount in investment C at k% simple annual interest. If the percent interest rates i, j, and k are in a ratio of 3:2:4, what is the ratio of the average rate of interest on all three investments (taken together) to the interest rate on investment A?

1) The amounts Saul invested in investments A, B, and C are in a ratio of 1:4:5.

2) Saul’s three investments total $100,000, while the total amount of money he earns in interest in the first year is $18,600

The OA is A

Note that we need to find out the weighted average of the three rates, i, j, and k, else this question can be solved without even the help of any statement. The simple average of the three rates would be (i + j + k)/3 = (3k + 2k + 4k)/3 = 3k

So, the required answer would be 3k/3k = 1.

But this is not to be done. We need to calculate the weighted average, i.e., take into account the sums for respective investments.

Let's take each statement one by one.

1) The amounts Saul invested in investments A, B, and C are in a ratio of 1:4:5.

Say the investments A, B, and C are p, 4p, and 5p and the rates are 3k, 2k and 4k.

So, the weighted average of rates = [(p*3k) + (4p*2k) + (5p*4k)] / (p + 4p + 5p) = 3.1k

So, the required answer would be 3.1k/3k = 3.1/3. Sufficient

2) Saul’s three investments total $100,000, while the total amount of money he earns in interest in the first year is $18,600.

We have not information about investment B and C. We can't get the answer. Insufficient.

Correct answer: A

Hope this helps!

-Jay
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[deloitte247]

The ratio of interest rate of A, B, and C = i, j, and k%
i:j:k = 3:2 :4

Target question => What is the ratio of the average rate of interest on all three investments taken together to the interest rate on investment A?
$$i.e\ \frac{i+j+k}{3}\ :\ i$$

Statement 1 => The amount Saul invested in investments A, B, and C are in ratio of 1:4: 5
Assuming that investments A, B, and C are $100, $400 and $500 respectively
i% = 3% of $100 = $3
j% = 2% of $400 = $8
k% = 4% of $500 = $20
$$\ \frac{i+j+k}{3}\ :\ i$$
$$\ \frac{3+8+20}{3}\ :\ 3$$
$$=>\ \frac{31}{3}\div\frac{3}{1}$$
$$=>\ \frac{31}{3}\cdot\frac{1}{3}=\frac{31}{9}$$
Statement 1 is SUFFICIENT

Statement 2 => Saul's three investments total $100000, while the total amount of money he earns in interest in the first year is $18,600
Investments A + B + C = $100,000 but their ratio are unknown, so the value of i, j, and k cannot be estimated.
Statement 2 is NOT SUFFICIENT

Since only statement 1 is SUFFICIENT,
Answer = A