Bunuel wrote:
One fisherman was telling his friends that he caught a fish that had a 60 feet long head and a tail which was equal to the length of the head plus half the length of the body. If the body was half the length of the whole fish, what is the length of the fish?
A. 120
B. 200
C. 240
D. 400
E. 480
This is the sort of problem that lends itself to being solved backwards from the answers, but you still have to
make sure you answer the question that is being asked. Namely, we want to know the length of the
entire fish, not just the unknown length of its body.
Knowing that the tail is as long as the head
plus half the length of the body should make us think that a larger number, rather than a smaller one, would make more sense as a starting point. That is, 60 + 60 = 120 already, and that does not account for the 1/2 portion of the body plus the body itself. Thus, (D) would represent a logical guess. Why (D) over (C)? This is a debate I get into now and then with people who insist on starting with (C) to use as a gauge instead. To be sure, (C) is useful to that end; however, unless the answer is (C) itself or the two lower or higher answers are far apart enough for you to be able to pick one or the other, you will still have to work between two other answers--(A) and (B) or (D) and (E). Starting with a higher estimate in (D), for instance, gives you insight into whether that is the answer, of course, but it also tests (E) by default--if the answer had to be a higher number, then only (E) would suffice. Furthermore, if (D) were a little too high, then (C) would represent a logical answer. Starting with (B) or (D)
after reasoning which one represented a better entry point can save you time, more so than what I have observed with students who start with (C).
Anyway, back to the problem at hand. Assuming that the fish is 400 feet altogether, that means, working backward from the question, that the body length must be 200 feet. Stretching back even more, we can now deduce that the tail must be 60 + 100, or 160, feet in length. Do the numbers add up? With a head that is 60 feet, all we have to do is add up the parts: 60 (head) + 200 (body) + 160 (tail) = 420. Close, but no cigar.
For the sake of illustration, what if we went in the wrong direction now and tested (C) instead of (E)? If the fish were 240 feet in length, then the body would be 120 feet, and the tail would be 120 feet (60 + half of 120) as well. Now the entire fish would be 60 (head) + 120 (body) + 120 (tail) = 300. Whereas before, with (D), we were 20 feet off, now we are 60 feet off, so we know we need to add body length instead of decrease it.
If we wanted to test (E), 480, we could, applying the same process as before. If the fish were 480 feet long altogether, then the body would be 240 feet, and the tail would be 180 feet (60 + half of 240). Since 60 (head) + 240 (body) + 180 (tail) = 480, we know we have the right answer.
It may not be as quick or efficient as solving for an unknown through the official answer posted above, but if you ever draw a blank, at least leaning on logic can get you the correct answer in a reasonable amount of time.
Good luck with your studies.
- Andrew