Let n=1627423de be a base-ten numeral with d and e its last two digits.

Question

Let n=1627423de be a base-ten numeral with d and e its last two digits. Give all of the choices of the two-digit numbers de for which n is divisible by 12.

Answer 1

1> Find a multiple of 12 that is less than 162742300.

162742300 / 12 = 13561858 with remainder of 4

2> Multiply that number by 12 to find a multiple of 12:

13561858 * 12 = 162742296

3> Add 12 to find the first possible last two digits:

162742296 + 12 = 162742308

4> Then add 12 repeatedly:

08 20 32 44 56 68 80 92 104 116 128 140 152 164 176 188 200 ....

d can be {0,1,2,3,4,5,6,7,8,9}

e must be {0,2,4,6,8}

Repeats.

Answer 2

1*10^8

6*10^7

↓ ↓

d*10^1

e*10^0