Four options have been given out of which three are alike in some manner, while one is different. Choose the odd one.
75
Odd One Out: Number Properties Analysis
The question requires identifying the number that does not share a common property with the others among the options: 125, 75, 729, and 1331.
Number Analysis
Let's examine the mathematical properties of each number:
- 125: This number is a perfect cube. It can be expressed as $5^3$.
- 75: This number is not a perfect cube. Its prime factorization is $3 \times 5^2$.
- 729: This number is a perfect cube. It can be expressed as $9^3$.
- 1331: This number is a perfect cube. It can be expressed as $11^3$.
Identifying the Different Number
Three of the numbers (125, 729, and 1331) are perfect cubes:
- $125 = 5 \times 5 \times 5 = 5^3$
- $729 = 9 \times 9 \times 9 = 9^3$
- $1331 = 11 \times 11 \times 11 = 11^3$
The number 75 is not a perfect cube.
Therefore, 75 is the odd one out.
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