Question 17

You are asked if the specific value of the longest of the three pieces can be determined.

Statement (1) alone: If two pieces are each 1 meter shorter than the longest piece, you should proceed as follows:

1. Visualize three pieces of equal length.

2. After visualizing three pieces of equal length, you should visualize adding one meter to one of the three pieces.

3. If after having added the one meter to the third piece you the sum of the three pieces is 22, this means that the sum of the three equal pieces is 21. Therefore, before adding the extra meter to the third piece the three equal pieces must each be 7. After adding 1 to 7 the length of the longest piece will be 8.

For those who love the math, here we go.

Let x be the length of one of the shorter sides.

x + x + x + 1 = 22

3x + 1 = 22

3x = 21

x = 7

The longest piece is x + 1 which = 7 + 1 = 8.

Hence, the answer can be determined from (1) alone. You can eliminate (B), (C) and (E).

Statement (2) alone: If one piece is 7 meters long, the sum of the other two pieces is 15. There are numerous ways to make up a sum of 15. Here are some examples:

Example 1: 10 + 5 = 15. This would make the longest piece 10.

Example 2: 12 + 3 = 15. This would make the longest piece 12.

Therefore, the length of the longest piece cannot be determined from statement (2) alone.

Since, the answer can be determined from statement (1) alone and cannot be determined from statement (2) alone, the answer is (A).