JIPMAT 2023 (QA) - <p>Amicable numbers are a pair of distinct natural numbers (a, b) such that the sum of the proper divisors of a equals b and the sum of the proper divisors of b equals a. Given that (220, y) is a pair of amicable numbers, y equals:</p> | PYQs + Solutions | AfterBoards
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JIPMAT 2023

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Medium

Amicable numbers are a pair of distinct natural numbers (a, b) such that the sum of the proper divisors of a equals b and the sum of the proper divisors of b equals a. Given that (220, y) is a pair of amicable numbers, y equals:

Correct Option: 2
1) First, let's find all proper divisors of 220:\newline * Proper divisors are all positive divisors excluding the number itself\newline * Factors of 220 = 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220\newline * Proper divisors of 220 = 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110\newline * Sum of proper divisors of 220 = 284
2) Let's check each option:
If y = 225:\newline * Proper divisors of 225 = 1, 3, 5, 9, 15, 25, 45, 75\newline * Sum = 178\newline * Since 178 ≠ 220, 225 is not correct
If y = 284:\newline * Proper divisors of 284 = 1, 2, 4, 71, 142\newline * Sum = 220\newline * Since sum of proper divisors of 220 = 284 AND\newline * Sum of proper divisors of 284 = 220\newline * This makes (220, 284) an amicable pair!
No need to check 404 since we found our answer.
Therefore, y = 284.

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JIPMAT 2022

Given below are two statements:
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JIPMAT 2023

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