PrepLattice is an independent test-preparation service and is not affiliated with or endorsed by GMAC, the organization that administers the GMAT. GMAT and GMAT Focus are trademarks of GMAC, used here only to name the exam this question is designed to prepare you for.
A rectangular community garden plot has a length that is 4 meters longer than its width. If the area of the plot is 96 square meters, what is the width of the plot, in meters?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
B
Translate the two clauses into algebra. Let the width be w. The length is 4 meters longer, so the length is w + 4. The area is length times width, so (w + 4) × w = 96. Expanding gives w² + 4w = 96, or w² + 4w − 96 = 0. Factor: we need two numbers whose product is −96 and whose sum is 4, which are 12 and −8, so (w + 12)(w − 8) = 0. The roots are w = −12 and w = 8. A width cannot be negative, so discard w = −12 and keep w = 8. The width is 8 meters (and the length is 12 meters, which checks: 8 × 12 = 96). The answer is (B).
Why the wrong choices tempt you: (A) 6 comes from hunting for any factor pair of 96 and landing on 6 and 16, then reporting the smaller value, but 6 and 16 differ by 10, not the required 4. (C) 12 is the length, not the width, so it answers the wrong quantity; it also equals the size of the rejected negative root, so taking the wrong root leads here too. (D) 16 is the larger member of that same mis-selected 6-and-16 pair. (E) 24 comes from dividing the area by the 4-meter difference (96 ÷ 4 = 24), treating the difference as a divisor instead of building the quadratic. Only w = 8 satisfies both that the dimensions differ by 4 and that their product is 96.
Pick the theme that suits how you work. You can change it anytime.