Nancykgp wrote:
Quote:
On 1st January of a certain year, Jones invested a total of $10000 under simple interest in two different schemes. He invested one part at 5% p.a and the other part at 3% p.a. How much did he invest at 5% p.a?
(1) The difference in the total amounts of interests earned by the two investments at the end of 1 year from the date of the investments is $300.
(2) The difference of the amounts invested in the two schemes is $5000.
commodork71sing statement #1 and the prompt, we can write 2 equations for the 2 unknowns: X(1.05)-300= Y(1.03) and X+Y=10,000. As a rule, you need x amount of distinct equations to solve for x amount of variables. Thus, without solving the equations, you know there is sufficient information.
Using statement #2 and the prompt you can do the same thing: X+Y=10,000 and X-Y=7,000. Again, you would only need to recognize that you have 2 equations for 2 unknowns to see that it's sufficient.
Note that this rule only applies for distinct equations. What I mean by that is that both offer information that is not contained in the other. For example, if the equations you were given were X+Y=10,000 and 2(X+Y)=20,000, you really only have one useful equation.
So here the answer is that either are sufficient on their own.
From statement 1, we only know the difference which means, either X(1.05)-300= Y(1.03) OR X(1.05)+ 300= Y(1.03) which will give you two different answers. Isn't it ?
From statement 1, we only know the difference in interest, which implies either 0.05x - 300 = 0.03y or 0.05x + 300 = 0.03y, alongside x + y = 10,000. This is because we are told the difference in the interest earned was $300, not the difference in the balance. So, we'd have:
1. 0.05x - 300 = 0.03y and x + y = 10,000
Or
2. 0.05x + 300 = 0.03y and x + y = 10,000
Next, solving the second set gives x = 0 and y = 10,000, which would be unrealistic since we can infer that at least some amount was invested at 5%.