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 landscaping cooperative encloses a rectangular community plot using exactly 70 meters of fencing along its four sides. The enclosed plot has an area of 304 square meters. What is the length, in meters, of the longer side of the plot?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
B
Let the two side lengths be L and W. The perimeter gives 2(L + W) = 70, so L + W = 35. The area gives L × W = 304. The two sides are therefore the roots of the quadratic t² − 35t + 304 = 0.
Factor it by finding two numbers that multiply to 304 and add to 35: those numbers are 16 and 19, since 16 × 19 = 304 and 16 + 19 = 35. So (t − 16)(t − 19) = 0, giving sides of 16 and 19. The longer side is 19, which is the correct answer (B).
Choice (A) 16 is the smaller root: a solver who factors correctly but does not re-read which side is asked for picks the shorter side. Choice (C) 35 comes from halving the perimeter to get L + W and reporting that sum instead of a single side. Choice (D) 38 traps a solver who searches for any factor pair of 304 (here 8 and 38) and reports the larger factor without enforcing the sum-of-35 condition, so it satisfies the area but not the perimeter. Choice (E) 51 comes from forgetting to halve the perimeter, treating L + W as 70, and estimating one side from that inflated total. Only 19 satisfies both the perimeter and the area, so (B) is the single defensible answer.
Pick the theme that suits how you work. You can change it anytime.