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If a 4-digit number 13z4 is divisible by 6, then the greatest possible value of digit 'z' is:
1
4
3
7
7
A number is divisible by 6 if it is divisible by 2 and 3. It is already even (ends in 4), so check the sum of digits 1+3+z+4=8+z for multiples of 3. For the greatest value of z, test z=9,8,7 etc.
A 4-digit number 13z4 is divisible by 6.
n=2├Ч3
A number is divisible by 6 if it is divisible by 2 and 3. It is already even (ends in 4), so check the sum of digits 1+3+z+4=8+z for multiples of 3. For the greatest value of z, test z=9,8,7 etc.
Students often forget that the sum of digits must be a multiple of 3, not the digit itself, or they might pick 9 without checking the sum constraint.
Check Divisibility by 2
Since the number ends in 4, it is definitely divisible by 2 for any digit value of z.
13z4┬аends┬аin┬а4тЯ╣divisible┬аby┬а2
Check Divisibility by 3
For the number to be divisible by 6, it must also be divisible by 3. This means the sum of its digits must be a multiple of 3. The sum is 1+3+z+4=8+z.
(8+z)тЙб0(mod3)
Find the Greatest Value for z
We test values for z starting from the largest possible digit (9). If z=9, sum =8+9=17 (not divisible by 3). If z=8, sum =8+8=16 (not divisible by 3). If z=7, sum =8+7=15 (divisible by 3).
8+7=15=3├Ч5
D is correct because 7 is the largest single digit that makes the sum of digits 8+z divisible by 3.
Always verify divisibility by 6 by checking both factors 2 and 3; checking only one is a common error in competitive exams.
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