Find the odd number in the group: 111, 383, 263, 551
2016
Find the odd number in the group: 111, 383, 263, 551
Answer: B. 383 — Concept: a classification ("odd one out") group of numbers is built on a specific relation that the members share among their own digits, not on a property…
- A.
111
- B.
383
- C.
263
- D.
551
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Correct answer: B
Concept: a classification ("odd one out") group of numbers is built on a specific relation that the members share among their own digits, not on a property that merely happens to be unique to one member, because every number has some unique property. For a three-digit number with hundreds digit h, tens digit t and units digit u, one standard relation of this kind is t = h × u, that is, the middle digit equals the product of the two outer digits. The member that breaks the shared relation is the odd one. Note that "odd" here means the member that does not belong with the rest, not "odd" in the sense of parity: all four numbers offered are odd numbers.
Application: test the relation t = h × u on each number of the group.
Number | Outer digits | Product of the outer digits | Middle digit |
|---|---|---|---|
111 | 1 and 1 | 1 | 1 |
383 | 3 and 3 | 9 | 8 |
263 | 2 and 3 | 6 | 6 |
551 | 5 and 1 | 5 | 5 |
Three of the four numbers, namely 111, 263 and 551, satisfy t = h × u exactly. Only 383 does not: its outer digits give 3 × 3 = 9, while its middle digit is 8.
Cross-check: the other properties that are commonly tried on such a group do not define it.
Primality does not separate the group. 383 and 263 are prime, while 111 = 3 × 37 and 551 = 19 × 29 are composite, a two-two split that leaves no single member standing alone. (551 looks prime, but it is not.)
This item is drawn from the longer number group 331, 482, 551, 263, 383, 242, 111. Every member of that group except 383 satisfies t = h × u (3 × 1 = 3, 4 × 2 = 8, 5 × 1 = 5, 2 × 3 = 6, 2 × 2 = 4, 1 × 1 = 1), six numbers out of seven. That settles the digit relation as the rule the setter used, and 383 as the member that breaks it.
The observation that, among the four numbers offered here, only 111 is a multiple of 3 is a by-product of the shortened list rather than the group's rule. It is a property of a single member, and roughly two out of every three integers are non-multiples of 3, so it carries no information about how the group was built. The digit relation, by contrast, is a specific structural condition that the remaining members meet exactly.
So the odd number in the group is 383.