Lens 03 of 9
The cheap check
Look at a property that rules candidates out before any working: the last digit, parity, sign, size.
Most wrong answers can be killed by something far cheaper than solving. A product of two numbers ending in 7 and 3 must end in 1. A probability can't be negative. A number ending in 0 needs a factor of 5. Check the cheap thing first and most of the field disappears.
The clues that call for it
- Real Numbers
Can a power end in a certain digit?
6ⁿ = 2ⁿ × 3ⁿ has no factor 5, so it can never end in 0.
- Probability
Could this be a probability?
Anything below 0 or above 1 is out before you read the rest.
- Anywhere
Four options, one product
17 × 23 must end in 1: that alone kills half the options.
Worked example
Which of these is 17 × 23? 371 · 391 · 396 · 400
- 1
Start with all candidates
Four options, no multiplication yet.
- 371
- 391
- 396
- 400
- 2
Filter 1: the last digit
7 × 3 = 21, so the product must end in 1.
units(17 × 23) = 1
- 371
- 391
- 396
- 400
- 3
Filter 2: rough size
17 × 23 is a shade under 20 × 20 = 400, but well above 350.
- 371
- 391
- 4
Answer
391, reached without ever completing the multiplication.
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