The largest five-digit number which when divided by 7, 9 and 11, leaves the same remainder as 3 in each case, is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 99795.
Given :
Numbers = 7, 9, 11
Remainder in each case = 3
Concept Used:
The largest number which when divided by 7, 9 and 11, leaves the same remainder as 3 in each case is obtained by subtracting the (LCM - 3) from the largest number.
Explanation:
The largest five digit number = 99999
Now, LCM of(7, 9, 11) = 693
When divided by 693, 99999 will leave the remainder as 207
The largest 5-digit number which is divisible by 693 = 99999 - 207 = 99792
Now, as it leaves remainder 3 in each case, the required number = 99792 + 3 = 99795
Hence the number which when divided by 7, 9 and 11, leaves the same remainder as 3 in each case, is 99795.