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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Question : M is the largest 4-digit number which, when divided by 4, 5, 6, and 7, leaves the remainder as 2, 3, 4, and 5, respectively. What will be the remainder when M is divided by 9?
Question : Find the least number which when divided by 12, 18, 24, and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Question : Let $x$ be the least number which, when divided by 5, 6, 7, and 8, leaves a remainder of 3 in each case, but when divided by 9, leaves no remainder. The sum of the digits of $x$ is:
Question : A number when divided by 7 leaves a remainder of 4. If the square of the same number is divided by 7, then what is the remainder?
Question : On dividing a certain number by 363, we get 17 as the remainder. What will be the remainder when the same number is divided by 11?
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