Problem Solving

Hi AAPL,

We're told that a a rectangular yard is 20 yards wide and 40 yards long and that it is surrounded by a thick hedge that grows on the border of the property (but completely WITHIN the boundaries of the yard) and the hedge covers an area of 171 square yards. We're asked for the width of the hedge.

While the prompt doesn't state it, we're meant to assume that the hedge has a 'uniform width' that runs the entire perimeter of the rectangular yard. In visual terms, the overall rectangular yard is (20)(40) = 800 square yards, then there is a uniform hedge that takes up 171 of those square yards - leaving a smaller rectangular space that totals 800 - 171 = 629 square yards. This question can be solved in a number of different ways. Here's how you can use Number Properties and a bit of logic to get to the correct answer:

Since the hedge is uniform width, we know that the 'math impact' on the length and width of the overall yard will be the same. Thus, we can create the following formula for the area of the smaller rectangle that is created by the hedge:

(20 - X)(40 - X) = 629 where X represents the total width of the hedges on the top/bottom and left/right sides of the yard.

629 is a rather specific number, so it's likely that the two dimensions of the smaller rectangle are integers (as opposed to two non-integers). Based on the formula, we're subtracting the same value from 20 and 40, so the units digit of both numbers would be the SAME (19 and 39, 18 and 38, 17 and 37, etc.). For that product to end in a units digit of 9, the units digit of the length and width would have to be either 3 or 7... so let's see what happens when we test those possibilities:

(13)(33) = 429
(17)(37) = 629

629 is an exact match for what we were told, so the dimensions of the smaller rectangle MUST be 17 and 37. This means that the hedge MUST have a width of 1.5 yards (since we have to account for the hedge on all 4 sides of the rectangle).

Final Answer: C

GMAT assassins aren't born, they're made,
Rich