Question

Which number is divisible by 2, 3, 4, and 6?
A.124
B.3,072
C.1,005
D.786

Answer 1

1005 and 786 are not divisible by 4

Answer 2

and 124 is not divisible by 6

Answer 3

does that ^^ help ?

Answer 4

A number is divisible by 4 if the last two digits are divisible by 4. A number is divisible by three if the sum of its digits is divisible by 3. Any number which meets both of these criteria will also be divisible by 2 and 6.

Answer 5

For the divisible by 4 rule: Any number of the form: "abcdxy" can be re-written as:
100*"abcd" + xy. Since 100 is divisible by 4 (4*25), 100*"abcd" is always divisible by 4. Thus any time xy is divisible by 4, abcdxy will be divisible by 4.

Answer 6

For the divisible by 3 rule: Any number of the form "abcde" can be re-written as:
10000*a + 1000*b + 100*c + 10*d + e
9999a+a+999b+b+99c+c+9d+d+e
(9999a+999b+99c+9d)+(a+b+c+d+e)
9*(1111a+111b+11c+d)+(a+b+c+d+e)
Since 9*(1111a+111b+11c+d) is always divisible by 3 (and 9), abcde will be divisible by 3 (or 9) any time (a+b+c+d+e) is divisible by 3 (or 9).