On 1st January of a certain year, Jones invested a total of $10000 u

 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.