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121 : 169 :: 289 : ?...

121 : 169 :: 289 : ?

A

324

B

361

C

400

D

441

Text Solution

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The correct Answer is:
To solve the analogy problem 121 : 169 :: 289 : ?, we will analyze the first pair of numbers and find a pattern that can be applied to the second pair. ### Step-by-Step Solution: 1. **Identify the first pair**: The first pair of numbers is 121 and 169. 2. **Find the square roots**: - The square root of 121 is 11 (since \(11^2 = 121\)). - The square root of 169 is 13 (since \(13^2 = 169\)). 3. **Identify the relationship**: - We see that 11 and 13 are consecutive prime numbers. 4. **Identify the second pair**: The second number in the pair is 289. 5. **Find the square root of 289**: - The square root of 289 is 17 (since \(17^2 = 289\)). 6. **Determine the next prime number**: - The prime numbers following 11 and 13 are 17 and the next prime number after 17 is 19. 7. **Find the value for the quotient mark**: - Since 289 corresponds to 17, we can conclude that the number corresponding to the quotient mark should be the square of the next prime number, which is 19. - Therefore, the value we are looking for is \(19^2 = 361\). ### Final Answer: The answer to the analogy 121 : 169 :: 289 : ? is **361**. ---
To solve the analogy problem 121 : 169 :: 289 : ?, we will analyze the first pair of numbers and find a pattern that can be applied to the second pair. ### Step-by-Step Solution: 1. **Identify the first pair**: The first pair of numbers is 121 and 169. 2. **Find the square roots**: - The square root of 121 is 11 (since \(11^2 = 121\)). ...
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