Question

The length of a rectangle is increased by 60%. What should be the measure of new width to maintain the same area?
Statement 1: Percent reduction in width is 37.5%
Statement 2: Area of rectangle is 450 sq.m

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If neither statement (1) nor statement (2) suffices to answer the question

Hint:

Check whether statement 1's 37.5% is genuinely new information, or something already forced by the 60% length increase and equal-area condition.

Answer 1

The Correct Option is D

Step 1: Understand what is actually being asked.
The new length is 1.6 times the old length (a 60% increase). If we call the old length L and old width W, the new width W' must satisfy \(1.6L \times W' = L \times W\), because the area is kept the same.
This simplifies to \(W' = W/1.6 = 0.625W\), which just says the new width is 62.5% of the old width, a purely relative fact. To state an actual measured value for the new width, we need real numbers for L and W, not just this ratio.

Step 2: Check statement 1 alone.
Statement 1 says the percent reduction in width is 37.5%, which means new width = 62.5% of old width.
But this is exactly the same relationship that follows automatically from keeping the length increase at 60% and the area fixed, as shown in Step 1. It adds no new numeric information and never gives an actual measured width.
So statement 1 alone cannot produce a numeric value for the new width.

Step 3: Check statement 2 alone.
Statement 2 says the area of the rectangle is 450 sq.m.
This gives one equation, \(L \times W = 450\), but there are two unknowns, the original length and width, and only this one equation connecting them.
Without knowing either the original length or width individually, the actual new width cannot be pinned to one number.
So statement 2 alone is not sufficient either.

Step 4: Check both statements together.
Statement 1 only restates the ratio already implied by the problem, so it adds no independent equation. Combining it with statement 2 still leaves the single equation \(L \times W = 450\) with two unknowns.
There is still no way to compute one specific numeric value for the new width, even using both statements together.

Final Answer:
Neither statement alone, nor the two together, gives enough information to state an actual numeric width. \[ \boxed{\text{e - neither statement suffices}} \]