Twenty-Five Seconds at the Table
The table below appears in a speeded test booklet. You are allowed 25 seconds per item and no calculator; scratch work must be mental or a single line of figures. Rounding to the nearest minute is permitted, but in each item the two closest options differ by less than 5 percent, so careless rounding can flip the answer.
| Sortie | Taxi (min) | Airborne (min) | Turnaround (min) |
|---|---|---|---|
| A | 12 | 95 | 40 |
| B | 18 | 88 | 35 |
| C | 9 | 110 | 50 |
| D | 15 | 102 | 30 |
| E | 21 | 84 | 45 |
| F | 10 | 99 | 55 |
1. Which sortie has the largest airborne-minus-taxi difference, and how do you get there inside 25 seconds?
Read the worked answer
Do not compute all six sums. Compare the two columns row by row and notice the pattern:
- A: 95 vs 12 - gap about 83
- B: 88 vs 18 - gap about 70 (big taxi, small airborne: eliminate)
- C: 110 vs 9 - gap about 101
- D: 102 vs 15 - gap about 87
- E: 84 vs 21 - gap about 63 (eliminate)
- F: 99 vs 10 - gap about 89
B and E are killed instantly by inspection. C leads on the airborne column and has the smallest taxi time, so it wins on both counts without subtraction. D and F are close but each loses one of the two columns to C.
Answer: C, about 101 minutes.
The time-saver was eliminating on one column before subtracting on any.
2. Which sortie has the highest turnaround-to-airborne ratio, and why is the runner-up the dangerous choice?
Read the worked answer
Ratios:
| Sortie | Turnaround / Airborne |
|---|---|
| A | 40/95 = 0.42 |
| B | 35/88 = 0.40 |
| C | 50/110 = 0.45 |
| D | 30/102 = 0.29 |
| E | 45/84 = 0.54 |
| F | 55/99 = 0.56 |
D drops out immediately (smallest turnaround on the largest airborne time). The real contest is E versus F, and the gap is under 4 percent. Eyeballing favors F (the biggest turnaround in the table), but E has a much smaller denominator, which inflates its ratio.
Verify without decimals by cross-multiplying:
55 x 84 = 4,620 (F) versus 45 x 99 = 4,455 (E).
Numerator-over-numerator versus denominator-over-denominator settles it in one line: F wins.
Eyeballing the largest numerator would have produced E, which is the trap the item is built around.
3. Give a decision rule for spending 25 seconds on any table item.
Read the worked answer
- Read the question's operation before reading the table. Subtraction, sum, ratio, and extremum each let you skip different rows.
- Eliminate on one column first. A row that loses badly on the numerator or the denominator cannot win regardless of the other column.
- For ratios, never compare eyeballed decimals; cross-multiply. Two products of two-digit numbers take about the same time as one long division and are far less error-prone.
- Default to the extreme numerator only until a small denominator appears. That is precisely where eyeball answers fail.
- If you are past 20 seconds with no answer, mark and move. One guessed item costs less than two items you never reached.