achloes
avigutman Could a reasoning-based approach work for such a question? If so, how would you go about it?
Took me over 4 mins to go through the math, only to get it wrong
Certainly, no need for pen and paper here
achloes.
The free info describes a weighted average scenario: the $354 must lie somewhere in between 12% and 14% of the total amount invested (consider the extremes - if Pamela invested nothing then $354 is 14% of the total investment, and if Joe invested nothing then $354 is 12% of the total investment).
We are asked whether its possible to find the total amount invested by the two people, and we can already say that it's somewhere in between those two extremes ($354/14% and $354/12%).
Statement (1) gives us the ratio of the two investments (1/4 of P = 1/5 of J, so P:J is 4:5). Would different ratios imply different total amounts of investment? Of course. Any change you make to the ratio in Pamela's favour, for example, would require a greater overall investment to keep the $354 in place, and vice versa. So, if we know what the ratio is, that can only correspond with one particular total amount invested. Sufficient.
Statement (2) gives us the difference between the two investments. Given this $300 difference, any change in overall investment would change the $354 (an upward change would push the interest up and vice versa). There can be only one overall investment that leads to exactly $354, given that the difference is set at $300.
If this isn't intuitive for you, think of it this way: Joe and Pamela invest the exact same amount, Joe at 7% annual and Pamela at 6% annual, for a total of 13% annual. Then, Joe decides to add ANOTHER $300 at 7% annual. If we just look at that extra $300 separately, and deduct the interest (14% of $300) from $354, the remainder ($312) must be 13% of (
the total amount invested - $300) so of course we can find what that
total amount invested is.