4.2 Tables, Schedules, and Word Problems
Key Takeaways
- Table questions are arithmetic questions with labels; row headings, column headings, footnotes, and units decide what should be added or compared.
- Schedule questions require base-60 time arithmetic, so convert long durations to minutes before converting back to a clock time.
- Word problems become easier when you identify the final question, list only useful quantities, choose the relationship, and estimate before calculating.
- Simple algebra helps when a missing number must balance a quota, total, schedule, budget, or proportional relationship.
- Error logs for applied math should record whether the miss came from table reading, time conversion, equation setup, or answer-choice rushing.
Read the Task Before the Details
Applied math questions often hide a simple calculation inside a work scenario. Read the final sentence first so you know the target. Then return to the table, schedule, or paragraph and collect only the numbers that answer that target. This prevents the common mistake of adding every number just because it appears in the problem.
A good setup line includes the unit. Write "applications on Thursday," "minutes until closing," or "forms per mailing" instead of a bare number. On timed exams, labels keep your mind from switching columns, mixing days, or solving for a total when the question asks for a difference.
Table Strategy
Tables test attention to structure. Always inspect the title, row labels, column labels, and any units before doing arithmetic. Decide whether the question asks for a row total, a column total, a comparison, a maximum, a minimum, or a missing entry.
| Table task | What to compare | Common trap |
|---|---|---|
| Row total | entries across one row | accidentally include another row |
| Column total | entries down one column | miss a category in the column |
| Difference | two matching entries | subtract unrelated units |
| Largest or smallest | same row or same column only | compare totals with parts |
| Missing value | required total minus known parts | divide when subtraction is needed |
Worked Example: Service Table
Suppose a table lists Monday transactions: 38 new applications, 44 renewals, and 17 information requests. The Monday total is 38 + 44 + 17 = 99 transactions. If the question asks which category had the most transactions, compare 38, 44, and 17. Do not compare Monday's total with a category count from another day.
Schedule Arithmetic
Clock problems use 60 minutes per hour, not 100. When a question gives several durations, convert each duration to minutes, add or subtract, and then convert back to clock time. This method is slower at first but prevents errors such as treating 1 hour 45 minutes as 1.45 hours.
| Schedule setup | Example | Action |
|---|---|---|
| Start plus duration | 8:35 a.m. plus 95 minutes | add hours and remaining minutes |
| End minus duration | due at 4:10 p.m., takes 70 minutes | subtract minutes from due time |
| Time between events | 9:20 a.m. to 1:05 p.m. | count to the next hour, then add |
| Break included | two work blocks plus lunch | add only breaks that the question includes |
Worked Example: Finish Time
A clerk begins scanning at 9:42 a.m. The first batch takes 38 minutes, quality check takes 16 minutes, and the second batch takes 52 minutes. The total duration is 38 + 16 + 52 = 106 minutes, or 1 hour 46 minutes. The finish time is 11:28 a.m.
Word Problem Translation
Turn each word problem into a short work order. First, write the asked-for quantity. Second, list useful numbers with units. Third, choose a relationship: add, subtract, multiply, divide, use a rate, or set up a simple equation. Fourth, estimate before solving so an answer choice that is far too large or small stands out.
Worked Example: Missing Mailing Size
A benefits unit must send 210 letters. It holds 18 letters for supervisor review and divides the rest equally among 4 mailing trays. Let x be letters per tray. The equation is 4x = 210 - 18, so 4x = 192 and x = 48 letters per tray. The subtraction happens before division because held letters are not mailed.
Setup Table for Word Problems
| Question phrase | Likely relationship | Setup habit |
|---|---|---|
| "How many remain?" | original minus used | identify the original amount |
| "At this rate" | proportion or unit rate | find per one unit first |
| "Equally among" | division | subtract exclusions first |
| "No later than" | deadline minus duration | work backward from due time |
| "How many more" | difference | keep categories matched |
Error-Log Guidance
For table and schedule practice, your log should capture the reading move that failed. Write entries such as "used weekly total instead of Thursday column," "added lunch even though it was excluded," or "forgot to convert 75 minutes to 1 hour 15 minutes." These notes are more useful than writing "careless mistake."
If you miss several table questions, slow down and point to the row and column intersection before calculating. If you miss schedule questions, drill converting minutes to hours and minutes until the conversion is automatic. Applied math improves when the setup becomes routine.
A table shows Wednesday visitors by counter: Counter A had 37, Counter B had 29, Counter C had 46, and Counter D had 18. What was the Wednesday total?
A records review starts at 2:18 p.m. and includes a 42-minute file check, a 25-minute supervisor review, and a 33-minute data update. What time does it end?
A clerk has 156 notices. Twelve are returned as undeliverable, and the rest are placed equally into 6 outgoing batches. How many notices are in each batch?