Rates and Work: Make a TABLE

Say it's 9:40 at night. You finished work, answered the last email and finally opened your Quant practice. The question: one pipe fills a tank in 6 hours, another fills it in 3. How long do they take together? Your brain grabs the two numbers, smushes them into something in the middle, and says "about 4.5 hours." You click. You move on. You're WRONG. Two pipes working together are FASTER than either one alone. The real answer is 2 hours.

I watch this happen every single week. Smart people. People who run budgets and manage teams. They see a rate question on the Executive Assessment, try to juggle it in their heads, and drop the ball. Here's the blunt verdict: rate and work questions are NOT hard. They are just messy. Draw one small table and they become some of the most routine points on the test.

Why these questions eat your clock

The Quant section of the Executive Assessment gives you 14 questions in 30 minutes. That's a little over 2 minutes per question, on average. Some are Problem Solving: a normal math question with five answer choices. Some are Data Sufficiency: you're given a question and two facts, and you decide whether those facts are ENOUGH to answer it. The test is adaptive section by section, which means it adjusts its difficulty based on how you're performing.

Now think about what a rate question asks you to hold. Two speeds. Two times. A distance. Maybe a switch from minutes to hours. That's five or six numbers. Stop reading for a second and answer honestly: how many numbers can you hold in your head while you also read five answer choices, late at night, after a full workday? I'll bet it's FEWER than you think.

And when you lose one, you reread the question. Then you redo the math. That's where the 4 minute rate question comes from. Pacing is not the disease here. It's the symptom. The disease is doing the work in your head. Fix that and the clock fixes itself.

The table

Every rate question runs on one rule: Rate × Time = Amount. A rate is just how much gets done per unit of time. Miles per hour. Tanks per hour. Reports per day. For travel, the Amount is distance. For work, the Amount is the job.

So the table on your scratch paper has three columns: Rate, Time, Amount. One row for each person, machine or leg of the trip. Add a Total row if the question combines them. That's the whole tool. Three rules make it work:

• Two boxes give you the third. In any row, if you know two of the three, multiply or divide to get the last one.
• Things working together ADD their rates. Never their times.
• Totals come from the Time and Amount columns. Add those down, then divide. NEVER average the Rate column.

One more move. If the question never tells you the size of the job or the distance, pick one. Pick a number that every time in the problem divides into evenly. That's the least common multiple, one of those number properties you already know. Now you're working with whole numbers instead of fractions.

Work questions are the same table

Work questions scare people because the rates are fractions. A machine that finishes a job in 6 hours has a rate of 1/6 of the job per hour. Fractions in your head at 9:40 at night? No thanks. Pick a job size and the fractions disappear.

The mistakes I see every week

1. Averaging the speeds. 40 and 60 become 50 in your head because it feels fair. INSTEAD: add the Amount column, add the Time column, divide. Every time.
2. Adding the times. "A takes 6 hours, B takes 3, so together it's 9." Two pipes don't make the job slower. INSTEAD: things working together add RATES. Give each its own row, then add the rates in the Total row.
3. Mixing units. One speed is in miles per hour, one time is in minutes, and you multiply them anyway. INSTEAD: write the unit at the top of each column and convert before you fill a box.
4. Living with fractions. You fight 1/6 + 1/3 when you didn't have to. INSTEAD: pick a job size that every time divides into, and work in whole units.
5. Skipping the table because the question looks easy. That's pride, and pride is the most common ceiling I see. INSTEAD: draw it on EVERY rate and work question. It takes about 15 seconds. Rereading a question you didn't write down takes longer.

What's MORE important to you?

You have to decide what you want MORE: a strong Quant score, or the feeling that you're too sharp to need scratch paper. You can't have both. The test gives you the score you EARN, and on rate questions you earn it with three columns and a pencil.

So here's your job for today. Pull three rate or work questions you've already missed. Redo each one on paper with the table. No head math. Pick a number when one is missing. Then compare the new time to the old time. I'll bet you're faster AND right. Then do it again tomorrow with three new ones.