How many ordered pairs of positive integers (x, y) satisfy 2x + 3y < 18 ?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
QuantProblem Solving
Free GMAT Problem Solving Practice Question
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.
Answer & Explanation
Correct answer
C
For each positive integer x, y must be a positive integer with y < (18 − 2x)/3. Count the valid y-values row by row: x = 1 gives y < 5.33, so 5 values; x = 2 gives y < 4.67, so 4 values; x = 3 gives y < 4, so 3 values (the strict bound excludes y = 4); x = 4 gives y < 3.33, so 3 values; x = 5 gives y < 2.67, so 2 values; x = 6 gives y < 2, so 1 value; x = 7 gives y < 1.33, so 1 value; x = 8 and beyond give none, since y would have to be less than 0.67 or lower. Total = 5 + 4 + 3 + 3 + 2 + 1 + 1 = 19.
The strict-versus-inclusive boundary at each row is the load-bearing discipline: 2x + 3y < 18 never allows y to equal (18 − 2x)/3 exactly, only values strictly below it.