Question 533158: 1 find the least number between 200 and 500 which leaves a reminder of 3 in each case when devided by 8,10,12 and 30
2 find the smallest number which when devided by 12,15,18 and 27leaves a reminder 8,11,14 and 23.
3 fine the 5 digit greatest number devided by 25, 30, and 40 leaves a reminder of 20,25 and 35 respectively
4 what is the least number that must be added to 2000so that the sum is devided exactly by 10,12,16 and 18
5 four bells toll after interval of 8,9,12 and 15 minutes respectively if the toll together is 3 pmwhen they will toll together.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 1) If a number, n, leaves a reminder of 3 in each case when divided by 8, 10, 12 and 30, then n-3 must be divisible by 8, 10, 12 and 30. It must be divisible by their minimum common multiple, 120. The least number between 200 and 500 which complies, with n-3=240, is 243.
2) A number n, which when divided by 12, 15, 18 and 27 leaves a reminder 8, 11, 14 and 23 is 4 short of a multiple of all those numbers. Then n+4 must be a multiple of 540. The smallest number that complies, with n+4=540, is n=536.
3) A number n, that divided by 25, 30, and 40 leaves a reminder of 20, 25 and 35 respectively is 5 short of a multiple of all those numbers. A number n+5 that is multiple of all those numbers, must be a multiple of their minimum common multiple, 600. The two consecutive multiples of 600 flanking 100,000 are
n+5=166*600=99600 and n+5=167*600=100,400, corresponding to n=99595 and n=100,195. The 5 digit greatest number that complies with the requirements is n=99595.
4) What is the least number that must be added to 2000 so that the sum is divided exactly by 10, 12, 16 and 18. That sum must be a multiple of the minimum common multiple of 10, 12, 16 and 18,720. The least multiple of 720 greater than 2000 is 2160=2000+160. So the solution is 160.
5) Four bells toll after intervals of 8, 9, 12 and 15 minutes respectively. If the toll together is 3 pm, when they will toll together? The bells will toll together at intervals multiples of the minimum common multiple of 8, 9, 12 and 15, which is 360. Since 360 minutes is 6 hours, if the bells toll together at 3PM, the next time they toll together will be 9 PM.
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