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
Correct Answer: 1683
Solution : The LCM of 5, 6, 7, and 8 is 840. If 3 is added to 840 it becomes 843, which, when divided by 5, 6, 7, and 8, leaves the remainder of 3. 843 is not completely divisible by 9 and hence, we will take multiples of 840 The required number will be in the form of 840K + 3 (where K is any integer) After putting K = 2, we get 1683 which is completely divisible by 9. Hence, the correct answer is 1683.
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Question : Let $x$ be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but $x$ is divisible by 11. The sum of the digits of $x$ is
Option 1: 5
Option 2: 6
Option 3: 9
Option 4: 4
Question : Which of the following numbers leaves the remainder equal to the highest common factor of 6, 8, and 9, when divided by 6, 8 and 9?
Option 1: 291
Option 2: 575
Option 3: 506
Option 4: 433
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
Question : Let $x$ be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2000 and 2500, then what is the sum of the digits of $x$?
Option 1: 4
Option 2: 15
Option 4: 10
Question : A number when divided by 44 gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31?
Option 1: 3
Option 2: 4
Option 3: 5
Option 4: 6
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