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Q: What is the smallest number greater than 3000 which when divided by 4, 7 and 10, leaves remainders of 3, 6 and 9 respectively?
  • A. 3079
  • B. 3080
  • C. 3081
  • D. 3101
Correct Answer: Option A - According to the question, Remainder = 4 – 3 = 1, 7 – 6 = 1, 10 – 9 = 1 LCM of 4, 7 and 10 = 2 × 2 × 5 × 7 = 140 Let the number = 140 k -1 On putting k = 22, The required number = 140 × 22 – 1 = 3079
A. According to the question, Remainder = 4 – 3 = 1, 7 – 6 = 1, 10 – 9 = 1 LCM of 4, 7 and 10 = 2 × 2 × 5 × 7 = 140 Let the number = 140 k -1 On putting k = 22, The required number = 140 × 22 – 1 = 3079

Explanations:

According to the question, Remainder = 4 – 3 = 1, 7 – 6 = 1, 10 – 9 = 1 LCM of 4, 7 and 10 = 2 × 2 × 5 × 7 = 140 Let the number = 140 k -1 On putting k = 22, The required number = 140 × 22 – 1 = 3079