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Question 1 (nov.17th)

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Question 1 (nov.17th)

by bacali » Mon Nov 17, 2008 10:35 am
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 = 43y

(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.

OE: c
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Source: — Data Sufficiency |
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by mals24 » Mon Nov 17, 2008 10:56 am
let $a be the amount for which you receive x% interest

(60,000-a) amount for which you receive y% interest.

x%a+(60,000-a)*y% = 4080--->equ1
You have 3 unknown variables.

St 1: x = 43y

If you substitute it in equ 1 you'll still have 2 unknown variables y & a--> INSUFF

St 2: xa:(60,000-a)y = 3:2

Again you still have 3 unknown variables. ---> INSUFF

Combining the 2 statements

You have 3 unknown variables and 3 distinct equations. Hence you can solve and determine the value of x---> SUFF

Answer is C
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by gmat009 » Mon Nov 17, 2008 11:18 am
mals24 wrote:let $a be the amount for which you receive x% interest

(60,000-a) amount for which you receive y% interest.

x%a+(60,000-a)*y% = 4080--->equ1
You have 3 unknown variables.

St 1: x = 43y

If you substitute it in equ 1 you'll still have 2 unknown variables y & a--> INSUFF

St 2: xa:(60,000-a)y = 3:2

Again you still have 3 unknown variables. ---> INSUFF

Combining the 2 statements

You have 3 unknown variables and 3 distinct equations. Hence you can solve and determine the value of x---> SUFF

Answer is C
I also got equations similar to yours but when I am trying to solve all these I am getting E as answer.
Are you sure you are getting value of x after solving these equations and what value are you getting
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by mals24 » Mon Nov 17, 2008 12:07 pm
yup im getting a value for a as 2022
y = 2.8%
x= 1.204%

Im not sure of my calculations if they are correct. But you can find out the values of the 3 unknowns.

From st 1 you'll get an equation
x=43y
42ay+60,000y=408,000

From st 2 you'll get an equation

2xa=180,000y-3ay

Substitute x=43y in the above equation

you'll get 86ya=180,000-3ay
89ya=180,000y---equ 1
a=180,000/89 = 2022

Substitute in equ 1 youll get the value of y and then you can determine the value of x.
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