Problem Solving

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
A. 1 / r+2
B. 1 / 2r + 2
C. 1 / 3r + 2
D. 1 / r+3
E. 1 / 2r+3

It is of course possible to modelise the whole thing but I think that number picking is much more efficient here.

So let's assume Henry has 50 he gets 2 dollars for each dollar saved this year, then the solution is that he should spend 40 this year, save 10. Next year, he will have 20 which is 50% of 40. So the answer that we want is 1/5

Let's evaluate the potential answers:
A) 1 / R+2 = 1/3 --> OUT
B) 1 / 2R+2 = 1/4 --> OUT
C) 1/ 3R+2 = 1/5 --> OK
D) 1 / R+3 = 1/4 --> OUT
E) 1 / 2R+3 = 1/5 --> OK

Let's try another example:
If Henry has 80 and he gets 1.5 dollar for each dollar saved this year, then the solution is that he should save 60 so he keeps 20. Next year, he will have 30, which is 50% of 60. So the answer we want is 1/4.

C) 1 / 3R+2 = 1 / (3/2 + 2) = 1 / 7/2 = 2/7 --> OUT
E) 1 / 2R + 3 = 1/ (2/2 + 3) = 1 / (1+3) = 1/4 --> OK

So I think ans is E

And here is how to do it in a 'modelised' way.

If Henry has a 100, he will spend X and save Y.

We know that he will need to have half as much next year as this year. Therefore:
X = 2 Y (1+R)

We are looking for the share of the total that he needs to save:

Y / (X+Y) = Y / (2Y(1+R) + Y) = 1 / (2 + 2R + 1) = 1/(2R+3) --> ANS E