Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
Classic combined work rate question. X alone is 12 hours. Y and Z together: 1/15 + 1/18 = 6/90 + 5/90 = 11/90, so 90/11 hours. Ratio 12 / (90/11) = 12 * 11/90 = 132/90 = 22/15. Answer D.
Nice, I did the same but almost flipped the ratio at the end. Good thing I double-checked.
Wait, why is the ratio X's time to Y+Z's time 22/15, which is greater than 1? X takes 12 hours alone, and Y+Z take about 8.18 hours together. So X's time is longer, and 22/15 > 1 makes sense. I almost picked 15/22 because I swapped numerator and denominator.
Same trap. Always check which quantity goes in the numerator.
Got this right in about 90 seconds. The key is to not overthink; just use the standard 1/a + 1/b for combined rate and then take the reciprocal. I can see how the answer choices are designed to catch ratio reversals though.
Is there a shortcut without finding the LCM? Like can I just compare rates directly?
You still need the combined rate, but you can avoid the big LCM by noticing 1/15 + 1/18 = (18+15)/(15*18) = 33/270 = 11/90. Then ratio is 12/(90/11) = 22/15.
What it tests
Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.
Common trap
Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.