Odd One Out

The question is not "which one is different?" — several will be different in some way. The question is which single property is true of exactly three items and false of the fourth.

Test in this order:

1. Category. Are three of them fruits and one a vegetable, three states and one a city, three mammals and one a bird?
2. Number property. Run three checks in sequence: all prime, all perfect squares or cubes, all divisible by the same number. 121, 144, 169, 180, 196 are all squares except 180.
3. Letter groups. Look at the gaps between the letters. In BD, FH, JL, MP the gap is 2, 2, 2 and then 3.
4. Word structure. All the words may be anagrams of one another, or share a vowel pattern, or all end in the same suffix.

The single most common mistake is stopping at the first difference you notice. In 3, 5, 11, 14, 17 the number 14 is even, 3 is the smallest, 5 is the only multiple of 5, and 11 is the only one with two digits and equal digits — four "differences", but only one of them leaves a clean group of three: 3, 5, 11, 17 are all prime, so 14 is the answer.

How to check: state the shared property in words and confirm that it holds for all three of the others without exception.

Ask what exactly three share, not what one differs in · order of checks: category → prime / square / cube / divisibility → letter gaps → word structure · state the shared property in words before answering

Find the odd one out: 13, 17, 19, 21, 23. → Check the number properties in order. None is a perfect square or cube, so try primality: 13, 17, 19 and 23 have no factor other than 1 and themselves, while 21 = 3 × 7. Answer: 21. Sanity check: the shared property stated in words is "prime number", and it holds for all four of the others without exception, which is exactly the test a correct answer must pass.