Question
If 65x is a three-digit number and it is divisible by 6, what can be the value of the digit x?
Solution
If a number is divisible by 6, it must be divisible by both 2 and 3 In 65x, if this number is divisible by 2, the value of x must be even. So, it can be 0,2,4,6 or 8 65x is divisible by 3, If sum of its digits is a multiple of 3 6+5+x =11+x, if we put x =0, 11+0=11, not a multiple of 3 If put x =2, 11+2=13 not a multiple of 3 If put x =4, 11+4=15, is a multiple of 3 If put x =6, 11+6=17, not a multiple of 3 If put x =8, 11+8=19, not a multiple of 3 The value of x is 4.
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