Concept 5 of 5
Number Groups: Spot the Odd Statement
Today's big idea
Test each claim against every number in the group before calling it true.
One number that breaks a claim is enough to make the whole claim false.
How it works
👀 What's going on?
A handful of numbers is given, then several claims about them. Most of the claims hold, one does not, and the one that fails can fail on a single number out of four.
💡 Here's the trick
Look at the group above. Every claim has to be tried against every number in the group, not against the group's general look. A claim that all of them are even is destroyed by one odd number. A single exception makes the whole claim false.
🪄 How to do it
- 1.Read the numbers in the group above and keep them in front of you.
- 2.Take one claim and test it against each number in turn.
- 3.Stop that claim the moment one number breaks it, then move to the next.
✍️ Try it
For 5, 10, 15, 20, which is false: they all end in 0, they are all multiples of 5, or there are four of them? Then, for 3, 6, 9, 12, which is true: they are all odd, they are all multiples of 3, or the largest is 9?
In the first group they all end in 0 is false, because 5 and 15 do not. In the second, they are all multiples of 3 is true. The numbers mix odd and even, and the largest is 12.
⚠️ Watch out
You might be thinking a claim is true if most of the numbers fit it. One exception is enough to sink it. In 2, 4, 6, 7 the claim that all are even fails on the 7 alone, however even the rest look.
🌟 Why this matters
Testing a general statement against the actual cases, rather than against an impression, is careful thinking in miniature. One counter-example settles it.
Exam tip: Hunt for the one number that breaks a claim rather than checking the ones that fit.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Set {3, 5, 8, 9}. Which statement is FALSE? (a) two even numbers (b) 9 is largest (c) three odd numbers”
- 1
Look at the set
Even: only 8 (one). Odd: 3, 5, 9 (three). 🧮
- 2
Test each claim
'Two even' ✗ — there is only one. '9 is largest' ✓. 'Three odd numbers' ✓.
- 3
Answer ✓
False = It has two even numbers
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Check every statement against the real numbers in the set.
SET · ROUND 1 OF 3
Numbers: 3, 6, 9
Which is TRUE?
Quick check
✅ VERIFICATION
How many numbers must break a claim for the whole claim to be false?
⚡ Finish the activity above first to answer.
Keep going!