Question:medium

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

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Check whether statement 1's 37.5% is genuinely new information, or something already forced by the 60% length increase and equal-area condition.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If neither statement (1) nor statement (2) suffices to answer the question
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The Correct Option is D

Solution and Explanation

Step 1: Write the same-area condition as an equation.
Let the original length and width be L and W. New length = 1.6L. Keeping the same area means \(1.6L \times W_{new} = LW\), so \(W_{new} = W/1.6\).
This equation alone already tells us the new width must be 62.5% of W, no matter what the actual numbers are. So this specific percentage is not new information waiting to be supplied by a statement, it is a fact baked into the question.

Step 2: See what statement 1 changes.
Statement 1 says the percent reduction in width is 37.5%, i.e. new width is 62.5% of old width, precisely what we already found in Step 1 using only the question stem.
Since it repeats a fact we can derive without it, it supplies zero extra numeric data, and by itself can never produce an actual width value in any unit.

Step 3: See what statement 2 changes.
Statement 2 gives the area as 450 sq.m, i.e. \(LW = 450\).
That is one equation in two unknowns. We could pick L = 10, W = 45, or L = 15, W = 30, and both fit \(LW=450\) but give different actual new widths (\(45/1.6=28.125\) vs \(30/1.6=18.75\)). Since more than one pair fits, the actual new width is not fixed.

Step 4: Combine and conclude.
Even using both statements, we still only have the single equation \(LW=450\) (statement 1 gives no second independent equation), so multiple (L, W) pairs remain possible, and the actual new width still cannot be pinned to one number. Neither statement alone nor both together are enough. \[ \boxed{\text{e}} \]
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