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1. Find the least number of five digits which when divided by 40, 60, and 75 , leave remainders 31 ,51 and 66 respectively .
- A. 10196
- B. 10196
- C. 10196
- D. 10196
Answer: Option D
Explanation:
Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75) - 9}
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
10000/600, we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75) - 9}
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
10000/600, we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191
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