A piece of string 35 inches long is cut into three smaller pieces

This is a moderately difficult question on equations. However, what makes it slightly more dangerous than it actually is, is the fact that there are traps laid for the unsuspecting student.

Remember, there can only be ONE longest and ONE shortest piece.

Let us assume the length of the longest piece as c, the medium-sized piece as b and the shortest piece as a, as shown in the figure below:


From the question statement, we know that c = 3a. Therefore, a + b + 3a = 35, which gives us,
b = 35 – 4a.

Now, for all of you who say the answer is Option B because 4a has to be a multiple of 4 – think again. Nowhere in the question is it mentioned that the pieces are of integral length. So, if you take a=7 and mark B as the answer, you have fallen for the trap answer.
Also, the medium sized piece cannot be the same length as the SHORTEST piece.

From here on, we can adopt a strategy of equating 35 – 4a with the options and finding out the possible length.

If 35 – 4a = 5, then 4a = 30. This means, a = 7.5 and c = 22.5 which gives us b = 5. This is impossible as a has to be the shortest piece. Option A can be ruled out.

If 35 – 4a = 10, then 4a = 25, which gives us a = 6.25, c = 18.75 and b = 10. This satisfies all the conditions. Option C could be the answer, so let’s hold on to it.

If 35 – 4a = 16, then 4a = 19 which gives us a = 4.75, c = 14.25 and b = 16. This is again not possible since c has to be the longest piece and not b. Option D can be ruled out and on similar lines, option E also gets ruled out.

The correct answer option is C.

As we mentioned, in this question, it’s not only about finding the length of the medium sized piece; it’s about finding its length in such a way that the SHORTEST and the LONGEST pieces remain themselves. If you only try to find out the length, you will end up falling for the trap answers like B, A and D.

Hope this helps!

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