Three of the following four numbers are alike in a certain way and one is different. Pick the number that is different from the rest.
254
Finding the Different Number in a Series
This question asks us to identify the number that is different from the rest in a given set of four numbers. This type of problem tests our ability to find a pattern or rule that applies to a group of numbers, and identify the one that doesn't follow that rule. The given numbers are 254, 217, 126, and 189.
Let's examine the properties of these numbers to find a common pattern among three of them.
- 254
- 217
- 126
- 189
We can try looking for patterns like even/odd, sum of digits, perfect squares or cubes $\pm$ a number, or divisibility rules.
Checking for Divisibility by 7
Let's test if these numbers are divisible by 7.
- For 217: $217 \div 7$
| Calculation | Result |
|---|---|
| $217 \div 7$ | 31 |
217 is divisible by 7 ($217 = 7 \times 31$).
- For 126: $126 \div 7$
| Calculation | Result |
|---|---|
| $126 \div 7$ | 18 |
126 is divisible by 7 ($126 = 7 \times 18$).
- For 189: $189 \div 7$
| Calculation | Result |
|---|---|
| $189 \div 7$ | 27 |
189 is divisible by 7 ($189 = 7 \times 27$).
- For 254: $254 \div 7$
| Calculation | Result |
|---|---|
| $254 \div 7$ | $36$ with a remainder ($254 = 7 \times 36 + 2$) |
254 is NOT divisible by 7.
Based on this analysis, we can see that three numbers (217, 126, and 189) are divisible by 7, while one number (254) is not divisible by 7. This establishes a clear pattern where 254 is the number that does not fit the rule.
Conclusion
The numbers 217, 126, and 189 share the property of being divisible by 7. The number 254 does not share this property. Therefore, 254 is the number that is different from the rest.
Revision Table: Analyzing Number Properties
| Number | Divisible by 7? | Notes |
|---|---|---|
| 254 | No ($254 = 7 \times 36 + 2$) | Not divisible by 7 |
| 217 | Yes ($217 = 7 \times 31$) | Divisible by 7 |
| 126 | Yes ($126 = 7 \times 18$) | Divisible by 7 |
| 189 | Yes ($189 = 7 \times 27$) | Divisible by 7 |
Additional Information: Odd One Out Reasoning
Odd one out questions in reasoning test involve classifying a group of items (numbers, letters, words, figures) based on a common characteristic or rule. The goal is to identify the one item that does not belong to the group. Common patterns to look for include:
- Mathematical operations (addition, subtraction, multiplication, division).
- Properties of numbers (even/odd, prime/composite, perfect squares/cubes, divisibility rules).
- Sequences or series (arithmetic progression, geometric progression, etc.).
- Sum or product of digits.
- Arrangement or structure (for letters, words, or figures).
Finding the pattern often requires checking multiple possibilities until one fits three or more items in the set, leaving only one item that is different.
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