Concept:A number divisible by 72 must be divisible by both 8 and 9. For divisibility by 8, the last three digits must be divisible by 8. For divisibility by 9, the sum of all digits must be divisible by 9.
Explanation:Check each option by substituting values of
x and
y into the number
9471x9y2.
Option A:
x=3,
y=1 gives number 94713912. Sum of digits =
9+4+7+1+3+9+1+2=36, divisible by 9. Last three digits 912 ÷ 8 = 114, so divisible by 8. Hence divisible by 72.
Option B:
x=8,
y=5 gives 94718952. Sum =
9+4+7+1+8+9+5+2=45, divisible by 9. Last three digits 952 ÷ 8 = 119, divisible by 8. Hence divisible by 72.
Option C:
x=4,
y=9 gives 94714992. Sum =
9+4+7+1+4+9+9+2=45, divisible by 9. Last three digits 992 ÷ 8 = 124, divisible by 8. Hence divisible by 72.
Option D:
x=9,
y=5 gives 94719952. Sum =
9+4+7+1+9+9+5+2=46, not divisible by 9. Last three digits 952 divisible by 8, but fails the 9 condition. Hence not divisible by 72.
Only option D does not satisfy divisibility by 72.
Answer:Option D:
x=9 and
y=5 is not true.