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Choose the odd one out: (A) 121, (B) 169, (C) 196, (D) 289
121
169
196
289
196
Check for squares of consecutive prime numbers versus composite numbers to spot subtle classification patterns quickly.
Check for squares of consecutive prime numbers versus composite numbers to spot subtle classification patterns quickly.
Analyze the Numbers
Examine the given numbers: 121, 169, 196, and 289. Identify their square roots: 121 is 11 squared, 169 is 13 squared, 196 is 14 squared, and 289 is 17 squared.
Identify the Underlying Prime/Composite Rule
Look at the bases of the squares: 11, 13, 14, and 17. The numbers 11, 13, and 17 are prime numbers, whereas 14 is a composite number.
Confirm the Odd One Out
Since 196 is the square of 14 (a composite number), while the other three are squares of prime numbers, 196 is the odd one out.
A: 121 is the square of prime number 11, so it follows the primary prime-square rule. B: 169 is the square of prime number 13, so it follows the primary prime-square rule. D: 289 is the square of prime number 17, so it follows the primary prime-square rule.
C is correct because 196 is the square of 14 which is a composite number, whereas 121, 169, and 289 are squares of prime numbers 11, 13, and 17 respectively.
When all options are perfect squares, always check whether the bases follow properties like being prime, odd, or even numbers before looking at differences.
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