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 shipping clerk is loading whole pallets onto a truck. The number of pallets, n, satisfies two conditions: four more than twice the number of pallets is at most 30, and when the number of pallets is subtracted from 5 and that result is multiplied by 3, the product is less than negative 9. How many integer values of n are possible?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
C
Translate each condition into a linear inequality, then combine them. Condition 1: four more than twice the number of pallets is at most 30, so 2n + 4 ≤ 30. Subtract 4: 2n ≤ 26. Divide by 2: n ≤ 13. Condition 2: subtract n from 5, multiply by 3, and the product is less than negative 9, so 3(5 − n) < −9. Expand: 15 − 3n < −9. Subtract 15: −3n < −24. Now divide both sides by −3, and because you are dividing by a negative number you must reverse the inequality sign: n > 8.
Combine the two results: 8 < n ≤ 13. Since n must be a whole number of pallets, the possible values are 9, 10, 11, 12, and 13, which is 5 values. The credited answer is (C) 5.
Why each wrong choice is a tempting slip: (E) 7 is the classic error of not flipping the sign when dividing by negative 3, which turns n > 8 into n < 8 and yields the values 1 through 7. (D) 6 comes from flipping correctly but treating the lower boundary as included (n at least 8 instead of n greater than 8), which wrongly adds 8 to the list. (B) 4 comes from flipping correctly but reading the at-most condition as a strict less-than, which wrongly drops the value 13. (A) 3 comes from dropping the top value 13 by reading at most as a strict less-than, and also losing the value 9 by starting the count at 10, an extra off-by-one at the low end, leaving only 10, 11, and 12. Each distractor isolates a single, common reasoning error: a missed sign reversal, an included boundary, an excluded boundary, or a miscount at the ends of the range.
Pick the theme that suits how you work. You can change it anytime.