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Let x denote the greatest 4digit number which when divided by 6,7,8,9,10 leaves a remainder of 4,5,6,7,8 respectively. Then the sum of four digit of x is(1) 25 (2) 18 (3) 20 (4) 22
Solution : 6 – 4 = 27 – 5 = 28 – 6 = 29 – 7 = 210 – 8 = 2Number divisible by 6, 7, 8, 9 and 10 = LCM of 6, 7, 8, 9 and 10 = 2520But , X is the greatest 4 digit number. So, the multiples of 2520 will also be divisible by 6, 7, 8, 9 and 10.The greatest 4-digit number multiple of 2520 = 7560Now, if we substract 2 from 7560 , then when that number is divided by 6, 7, 8, 9 and 10 , it would leave remainder of 4, 5, 6 7 and 8 respectively.Hence , the required number = X = 7560 – 2 = 7558Sum of the digits of X = 7+5+5+8 = 25
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