Robin split a total of $24,000 - another interest question

[mgmat]

I'm having trouble solving the interest rate questions. I know the formulas but am not correctly answering the questions in this topic. Please help.

Question:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?
1. Each investment earns the same dollar amount of the interest annually.
2. Investment X earns 5 percent simple annual interest.

Answer is C.

I know for data sufficiency I don't need to do the math. But since this is a weak topic area for me, can you please also explain how to rephrase and how I can set up the math in case I had to solve it as a Problem Solving question? Any insight on this question would be great!

[Sudhan]

Question:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?
1. Each investment earns the same dollar amount of the interest annually.
2. Investment X earns 5 percent simple annual interest.



P=24k; P= X+Y
Interest= PNR/100;
Interest(X)= (24000-Y)*1*R/100; Interest( Y)= (24000-X)*1*R/100

What is X?

Using BDACE Grid:
2) R(X)= 5%
But we dont know how much is the investment Robin put into X. Hence INSUFF

1) Each investment earns the same $ amount of the interest annually.
Interest(X)= Interest (Y) but we dont know about the Rate of Interest for either X or Y. Hence INSUFF

Using 1 and 2,

we know the Interest Rate for X; Also the $ of Interest Earned Annually from X and Y are equal. There by we can find how much invested in Y.

Thanks

[RonPurewal]

I'm having trouble solving the interest rate questions. I know the formulas but am not correctly answering the questions in this topic. Please help.

Question:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?
1. Each investment earns the same dollar amount of the interest annually.
2. Investment X earns 5 percent simple annual interest.

Answer is C.

I know for data sufficiency I don't need to do the math. But since this is a weak topic area for me, can you please also explain how to rephrase and how I can set up the math in case I had to solve it as a Problem Solving question? Any insight on this question would be great!

ok:
first, find expressions for the interest on each of the two accounts:
interest on x = 0.07x
interest on y = (rate)(24000 - x)

(1) alone:
0.07x = (rate)(24000 - x)
this is one linear equation, with two unknowns, so it can't be solved uniquely.
insufficient

(2) alone:
interest on x = 0.07x
interest on y = 0.05(24000 - x)
but there's no equation relating these two things
insufficient

together:
0.07x = 0.05(24000 - x)
linear equation in one variable --> can be solved uniquely
sufficient

answer = c

[Halo3]

quick one

By saying (1) each investment earns the same $ amount of annual interest, isn't the statement implying that "each investment earns the same $ amount of annual interest [every year] not just the first one. i.e. if x and y were different and had different interest rates, but ended up earning the same amt of annual interest in the first year, than they would end up having to yield different dollar amounts of interest in subsequent years. i.e if the $ amount earned after the 1st year was the same, but the interest rates were different, the 2nd year would yield different $ amounts?

if this were the case, shouldn't A be correct? I know it's not, just tell me why I'm wrong.

[RonPurewal]

quick one

By saying (1) each investment earns the same $ amount of annual interest, isn't the statement implying that "each investment earns the same $ amount of annual interest [every year] not just the first one. i.e. if x and y were different and had different interest rates, but ended up earning the same amt of annual interest in the first year, than they would end up having to yield different dollar amounts of interest in subsequent years. i.e if the $ amount earned after the 1st year was the same, but the interest rates were different, the 2nd year would yield different $ amounts?

if this were the case, shouldn't A be correct? I know it's not, just tell me why I'm wrong.

this is simple interest.

simple interest is calculated by just multiplying the interest rate (as a decimal) by the original principal. it particular, it is not compound interest; i.e., the interest only accumulates on the money that was originally in the account at time zero. the interest money itself doesn't accumulate any interest (unlike in compound-interest investments, where interest accumulates on everything, including the newly accrued interest money).

because of this definition, the amount of simple interest is exactly the same every year for each investment. therefore, if the 2 investments accrue the same amount of simple interest in the first year, then they must accrue the same amount of simple interest in every year.

[700+]

first, find expressions for the interest on each of the two accounts:
interest on x = 0.07x
interest on y = (rate)(24000 - x)

The question says "If investment earns 7% simple annual interest...". I don't know if I'm missing out something over here but doesn't it mean the whole investment earns an annual interest of 7%?

(2) alone:
interest on x = 0.07x
interest on y = 0.05(24000 - x)
but there's no equation relating these two things
insufficient

Statement 2 says "Investment X earns 5 percent simple annual interest." So shouldn't interest on x = 0.05x?

[MannyRosas]

I agree with linzphilipv.
The question says "If investment earns 7% simple annual interest...".

Maybe this is right?

If I call
Ix: interest on investment X
Iy: interest on investment Y
we know
24000 = X + Y
0.07*24000 = Ix*X + Iy*Y
And need to know Y

(1) alone:
Ix*X = Iy*Y
If I bring it to the total investment:
0.07*24000 = Ix*X + Iy*Y
0.07*24000 = 2*Iy*Y
or
0.07*24000 = 2*Ix*X
One linear equation, with two unknowns, so it can't be solved uniquely.
insufficient

(2) alone:
Ix = 0.05
If I bring it to the total investment:
0.07*24000 = Ix*X + Iy*Y
0.07*24000 = 0.05*(24000-Y) + Iy*Y
One linear equation, with two unknowns, so it can't be solved uniquely.
insufficient

together:
0.07*24000 = Ix*X + Iy*Y
0.07*24000 = 2*Ix*X
0.07*24000 = 2*0.05*(24000-Y)
One linear equation in one variable --> can be solved uniquely
sufficient

answer = C

[RonPurewal]

Statement 2 says "Investment X earns 5 percent simple annual interest." So shouldn't interest on x = 0.05x?

i guess i switched x and y.

note that the original poster left the letter (x or y) out of the prompt, so i guess i just assumed that it was x. if it's the other way around, just switch all of the x's and y's and the solution will still be correct.

[deepak1990verma]

first, find expressions for the interest on each of the two accounts:
interest on x = 0.07x
interest on y = (rate)(24000 - x)

The question says "If investment earns 7% simple annual interest...". I don't know if I'm missing out something over here but doesn't it mean the whole investment earns an annual interest of 7%?

Ron,
I have the same doubt as '700+'.
shouldn't it be:
interest on x + interest on y = 0.07*24000 , since the problem says that the investment ( i believe its x+y) earns 7% simple annual interest.
What am I missing here???

Thanks

[RonPurewal]

as noted by one of the earlier posters, this problem has been transcribed incorrectly ("If investment earns 7% simple annual interest...")

what has almost certainly happened here is that the letter 'x' or 'y' is missing from between the bold-face words.
if this were meant to refer to the entire investment, then there would be missing words (e.g., "If the entire investment earns...")

GMAC is meticulous with the wording of questions, so there is no way this one has been transcribed properly.

[RonPurewal]

ok, tell you what, i'm going to lock this thread. if anyone has questions and can produce a correct transcription of this problem, go ahead and start a new thread.

thanks.