Question : The largest five-digit number which when divided by 7, 9, and 11, leaves the same remainder as 3 in each case, is:
Option 1: 95840
Option 2: 98685
Option 3: 96720
Option 4: 99795
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Correct Answer: 99795
Solution :
The number which is divisible by 7, 9, and 11 should be divisible by LCM of (7, 9, 11) = 7 × 9 × 11 = 693
Largest 5-digit number = 99999
Quotient when 99999 is divided by 693 = 144
Largest 5 digit number divisible by 693 = 144 × 693 = 99792
The largest 5-digit number is divisible by 693 and leaves the remainder as 3 = 99792 + 3 = 99795
Hence, the correct answer is 99795.
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