1. The problem involves determining divisibility of numbers by 4, 8, 11, and 12 using divisibility rules. 2. Divisibility rules used: - Divisible by 4: The last two digits form a number divisible by 4. - Divisible by 8: The last three digits form a number divisible by 8. - Divisible by 11: The difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11. - Divisible by 12: The number is divisible by both 3 and 4. 3. Answers: 1) 432 is divisible by 4 because the last two digits (32) are divisible by 4. Answer: A 2) Not divisible by 4 is 1 566 because last two digits 66 is not divisible by 4. Answer: B 3) Divisible by 11: - 418 653: Sum odd positions = 4+8+5=17, sum even positions=1+6+3=10, difference=7 (not multiple of 11) - 639 284: Sum odd=6+9+8=23, sum even=3+2+4=9, difference=14 (not multiple of 11) - 927 421: Sum odd=9+7+2=18, sum even=2+4+1=7, difference=11 (multiple of 11) Answer: C 4) Divisible by 12: - 39 628: sum digits=3+9+6+2+8=28 (not divisible by 3) - 54 936: sum digits=5+4+9+3+6=27 (divisible by 3) and last two digits 36 divisible by 4 - 76 924: sum digits=7+6+9+2+4=28 (not divisible by 3) Answer: B 5) 3 440 divisibility: - Divisible by 4: last two digits 40 divisible by 4 - Divisible by 8: last three digits 440 divisible by 8 Answer: A 6) 401 000 divisible by 8 because last three digits are zeros. Answer: B 7) Divisible by 8: - 7135 last three digits 135 not divisible by 8 - 7136 last three digits 136 divisible by 8 - 7200 last three digits 200 divisible by 8 - 7236 last three digits 236 not divisible by 8 Answer: B and C (only one choice allowed, so B) 8) 40 634 divisibility: - Divisible by 4: last two digits 34 not divisible by 4 - Divisible by 8: last three digits 634 not divisible by 8 - Divisible by 11: sum odd=4+6+4=14, sum even=0+3=3, difference=11 (multiple of 11) - Divisible by 12: no (not divisible by 3) Answer: C 9) Not divisible by 8: - 9 634 last three digits 634 not divisible by 8 - 8 168 last three digits 168 divisible by 8 - 5408 last three digits 408 divisible by 8 - 3 440 last three digits 440 divisible by 8 Answer: A 10) 3 936 divisibility: - Divisible by 8: last three digits 936 divisible by 8 - Divisible by 11: sum odd=3+3=6, sum even=9+6=15, difference=9 (not multiple of 11) - Divisible by 12: sum digits=3+9+3+6=21 divisible by 3 and last two digits 36 divisible by 4 Answer: B q_count: 10