Let x be the least number which when divided by 32, 48, 90 and 64, the…
2018
Let x be the least number which when divided by 32, 48, 90 and 64, the remainders are 20, 36, 78 and 52 respectively. What is the sum of digits of x?
- A.
18
- B.
20
- C.
21
- D.
24
Attempted by 16 students.
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Correct answer: D
1. Find the difference between each divisor and its respective remainder: (32 - 20) = 12, (48 - 36) = 12, (90 - 78) = 12, and (64 - 52) = 12. The difference is constant (k = 12). 2. Calculate the LCM of the divisors 32, 48, 90, and 64. Their prime factorization gives an LCM of 2880. 3. The required least number x is given by (LCM - k). So, x = 2880 - 12 = 2868. The sum of the digits of x is 2 + 8 + 6 + 8 = 24. Final Answer: Option D