Question : What is the greatest number of six digits, which when divided by each of 16, 24, 72, and 84 leaves the remainder 15?
Option 1: 999981
Option 2: 999951
Option 3: 999963
Option 4: 999915
Correct Answer: 999951
Solution : The least common multiple (LCM) of 16, 24, 72, and 84 is 1008. The greatest six-digit number is 999999. The greatest number less than 999999 which is divisible by 1008 is given by dividing 999999 by 1008 and taking the round down to the nearest whole number, then multiplying by 1008. This gives us 999936, which is the greatest six-digit number divisible by 1008. Finally, we add 15 to this number (since we want the number to leave a remainder of 15 when divided by 16, 24, 72, and 84), giving us 999951. Hence, the correct answer is 999951.
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Question : What is the sum of the digits of the least number which when divided by 15,18, and 36 leaves the same remainder 9 in each case and is divisible by 11?
Option 1: 15
Option 2: 16
Option 3: 18
Option 4: 17
Question : Which is the largest six-digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainder 8, 11, 16, 20 and 26 respectively.
Option 1: 999956
Option 2: 999982
Option 3: 999960
Option 4: 999964
Question : The least number, which when divided by 5, 6, 7 and 8 leaves a remainder of 3, but when divided by 9, leaves no remainder, is:
Option 1: 1677
Option 2: 1683
Option 3: 2523
Option 4: 3363
Question : Find the greatest number which when divided 261, 853, and 1221, leaves a remainder of 5 in each case.
Option 1: 19
Option 2: 18
Option 3: 17
Option 4: 16
Question : Find the least number which when divided by 4, 9, 12, and 15, leaves the remainder 3 in each case.
Option 1: 360
Option 2: 183
Option 3: 193
Option 4: 180
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