Question

The length of a rectangle is increased by 60%. What should be the measure of the new width to maintain the same area?

Statement 1: Percent reduction in width is 37.5%.
Statement 2: Area of the rectangle is 450 sq.m.

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• C. If the data in both the statements together are needed to answer the question.
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Check whether statement 1 gives NEW information, or is just algebra you could already derive from a 60% length increase.

Answer 1

Answer: (E)

Let the original length be L and original width be W, so the area is LW. The new length becomes 1.6L. To keep the area unchanged, the new width must be LW / 1.6L = W / 1.6 = 0.625W, which is a 37.5% reduction from W. This percentage relationship holds automatically for any L and W whatsoever, purely because the length went up by 60%.

Statement 1 says the percent reduction in width is 37.5%. This is exactly the value that follows algebraically from the question itself, so it adds no new information about the actual measurement of the new width in real units (like metres); it only confirms something we could already work out. So statement 1 alone cannot give an actual numeric width. Not sufficient.

Statement 2 gives the area as 450 sq.m, meaning LW = 450. But length and width individually could be many different pairs (for example 45 x 10, or 90 x 5, or 30 x 15) - all giving area 450 but different actual widths. Since the new width is 0.625W, we still need to know W itself, not just the product LW. So statement 2 alone is not sufficient.

Combining both statements does not help either: statement 1 is just a restatement of a fact already implied by the question, so combined with statement 2 we still only know LW = 450, with W undetermined. Since even together the actual new width cannot be pinned to a number, the answer is (e).