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If a 4-digit number 12z4 is divisible by 4, then the greatest possible value of 'z' is:
6
4
2
8
8
A number is divisible by 4 if its last two digits form a number divisible by 4. Here, the last two digits are z4. Test digits for z (0-9) such that (10z + 4) is a multiple of 4.
A 4-digit number 12z4, where z is an unknown digit, and the number is divisible by 4.
NтЙб0(mod4)тЯ╣last┬аtwo┬аdigitsтЙб0(mod4)
A number is divisible by 4 if its last two digits form a number divisible by 4. Here, the last two digits are z4. Test digits for z (0-9) such that (10z + 4) is a multiple of 4.
Confusing the divisibility rule for 4 with the rule for 8 (last 3 digits) or ignoring that 0 is a possible digit for z.
Analyze the Divisibility Rule for 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For the number 12z4, the last two digits form the number z4, which is 10z+4.
10z+4=4k
Evaluate potential values for z
We need to check which digits zтИИ{0,1,2,3,4,5,6,7,8,9} satisfy the condition that (10z+4) is divisible by 4.
410z+4тАЛ=2.5z+1
Test digits to find the greatest value
Testing values of z starting from the largest digit z=9: If z=9, 94/4=23.5 (No). If z=8, 84/4=21 (Yes). Since we want the greatest value, we stop at z=8.
z=8
D is correct because 8 is the largest digit that makes the last two digits 84, and 84 is divisible by 4.
This concept of looking at the last 'n' digits is universal: last 1 digit for 2, 5, 10; last 2 for 4, 25; last 3 for 8, 125.
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