Question 36

Let x denote the greatest 4-digit number which when divided by 6, 7, 8, 9 and 10 leaves a remainder of 4, 5, 6 7 and 8 respectively. Then, the sum of the four-digits of x is

Solution

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The least number which when divided by 6, 7, 8, 9 and 10 leaves a remainder of 4, 5, 6 7 and 8 respectively is LCM(6, 7, 8, 9, 10) -2

=2520-2= 2518

The number will be in the form of k * LCM(6, 7, 8, 9, 10) -2

When k = 3, the value of x =7558

When k = 4, the value of x =10078

So the value of x = 7558

Sum of the digits of x = 7+5+5+8= 25

A is the correct answer.

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