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another way to do OG problem?

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another way to do OG problem?

by fangtray » Sun Apr 29, 2012 11:56 pm
Hello, I am looking for an alternate way to do this problem that is not the same way as explained in the OG guide.

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 hte rate of y percent pe ryear. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

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

thanks!
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by mathbyvemuri » Mon Apr 30, 2012 1:36 am
I didn't go through the explantion given by OG, but the following is my approach:

Let the amount that earned interest at the rate of x percent is A
=> the amount that earned interest at the rate of x percent is 60,000-A

The total interest earned = Ax/100 + (60000-A)y/100 = 4080
=> Ax+(60000-A)y = 408000 ---- (I)

Now let us examine the statements:
statement(1): x = 3y/4
This alone is not sufficient because if we substitute this in the equation (I), it eliminates only one unknown and we will end up with an equation with two unknowns.

statement(2): A/(60000-A) = 3/2
This alone is also not sufficient because if we substitute this in the equation (I), it elimintes only one unknown and we will end up with an equation with two unknowns.

But if we use both the statements together we can find the value of as each statement eliminates one unique unknown.

Hence answer is "C"
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by sanju09 » Mon Apr 30, 2012 2:09 am
fangtray wrote:Hello, I am looking for an alternate way to do this problem that is not the same way as explained in the OG guide.

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 hte rate of y percent pe ryear. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

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

thanks!
I didn't see the OG's approach, following is how I see to it:


Let's say that $d earned simple annual interest at the rate of x percent per year, and the remaining $(60,000 - d) earned simple annual interest at the rate of y percent per year, such that the total interest earned by the $60,000 for that year =

$[(d x/100) + {(60,000 - d) y/100}] = $4,080 (Given). To find x from the equation

[(d x/100) + {(60,000 - d) y/100}] = 4,080,

we need to know the values of both d and y.

(1) A relation in x and y can reduce the single available equation into two variables, d and x, and x cannot be found uniquely. Insufficient

(2) With d:(60,000 - d) = 3:2, we can find d uniquely, and this can reduce the single available equation into two variables, x and y, and x cannot be found uniquely. Insufficient

Taking (1) and (2) together, we can put the value of d as obtained from (2) into the reduced equation in d and x as obtained from (1) [spoiler]to answer x uniquely. Sufficient

Take C[/spoiler]
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by GMATGuruNY » Mon Apr 30, 2012 4:16 am
fangtray wrote:Hello, I am looking for an alternate way to do this problem that is not the same way as explained in the OG guide.

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

thanks!
Since 4080 is between 5% and 10% of 60,000, it is likely that x and y are between 5 and 10.

Statement 1: x = (3/4)y
It's possible that x=6 and y=8 or that x=6.6 and that y=8.8.
To accommodate the desired combination of percentages, we could simply adjust the amount invested at each percentage so that the total amount of interest earned = 4080.
Since x can be different values, INSUFFICIENT.

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 3/2.
Sum of the parts of the ratio = 3+2 = 5.
Since the actual amount invested = 60,000, and 60,000/5 = 12000, the two parts of the ratio must be multiplied by 12,000:
12,000(3:2) = 36,000:24,000.
Thus, 36,000 earns x% interest and 24,000 earns y% interest.
It's possible that x=6 or that x=6.6.
To accommodate each value for x, we could simply adjust the value of y so that the total amount of interest earned = 4080.
Since x can be different values, INSUFFICIENT.

Statements 1 and 2 combined:
32,000 earns x% interest and 24,000 earns y% interest.
Since x=(3/4)y, for every 4% of interest earned by the $24,000, 3% interest is earned by the $36,000.
If x=3 and y=4:
(.03)(36,000) + (.04)(24,000) = 1080+960 = 2040.
Since 2040 is half the amount of interest needed, the percentages must be doubled to 6% and 8%.
Thus, x=6.
SUFFICIENT.

The correct answer is C.
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