Difficulty: Easy
Correct Answer: 8
Explanation:
Introduction / Context:
This question checks your understanding of perfect squares and perfect powers. You are given four numbers and asked to choose the one that does not belong with the others. Such odd number questions are common in aptitude tests because they assess basic number sense and knowledge of square numbers without involving long calculations.
Given Data / Assumptions:
- The options are 25, 49, 9, and 8.- All values are small integers suitable for quick mental checking.- The most natural classification to test here is whether the numbers are perfect squares.
Concept / Approach:
A perfect square is a number that can be written as n^2 for some integer n. Many exam questions use familiar squares such as 3^2, 5^2, and 7^2. The general strategy is to express each option as a square, if possible. The number that cannot be expressed as a perfect square, while the others can, will be the odd one out.
Step-by-Step Solution:
Step 1: 25 = 5^2, so it is a perfect square.Step 2: 49 = 7^2, so it is also a perfect square.Step 3: 9 = 3^2, another perfect square.Step 4: 8 is equal to 2^3 and is a perfect cube, not a perfect square.Step 5: Since three numbers are perfect squares and one is not, the non square is the odd number.
Verification / Alternative check:
You can list basic squares up to 10^2: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. In this list, 9, 25, and 49 clearly appear, but 8 does not. That quick check confirms that 8 is not a perfect square.
Why Other Options Are Wrong:
25: Lies in the square list as 5^2.49: Lies in the square list as 7^2.9: Lies in the square list as 3^2.
Common Pitfalls:
Some students confuse perfect cubes with perfect squares or rely only on memory without verifying. Always check by seeing if the number fits the pattern n^2. If not, do not assume it is a square.
Final Answer:
The odd number is 8 because it is a perfect cube, not a perfect square like the other three options.
Discussion & Comments