Answer:
98, 68, 44, 20
Explanation:
we can write the other two-digit number as:
a*10 + b
Where both a and b are single-digit numbers.
When we "attach" this at the right of 55, the number that we get is:
5500 + a*10 + b
And this number is divisible by 24 if it is divisible by 3 and 8.
A number is divisible by 8 if the sum of its digits is divisible by 3, then we must have:
5 + 5 + a + b = multiple of 3 = n*3
A number is divisible by 8 if the last 3 digits are divisible by 8, then:
500 + b*10 + a = multiple of 8 = m*8
First we can use the second relation to find the value of b:
500 + b*10 + a = m*8
so we need to find a multiple of 8 that is in the range (500, 599)
for example, if we use:
8*65 = 520
Then we have:
b = 2
a = 0
5504, 5512, 5520, 5528, 5536, 5544, 5552, 5560, 5568, 5576, 5584, 5582, 5590, 5598.
Now we just need to see if these are divisible by 4.
5504:
5 + 5 + 0 + 4 = 14
not divisible by 3.
5512:
5 + 5+ 1 + 2 = 13
not divisible by 13
5520:
5 + 5 + 2+ 0 = 12
divisible by 3, then 20 is a option.
5528:
5 + 5 + 2 + 8 = 20
not divisible by 3
5536:
5 + 5 + 3 + 6 = 19
not divisible by 3
5544:
5 + 5 + 4 + 4 = 18
is divisible by 3, then 44 is a option.
5552:
5 + 5 + 5+ 2 = 17
not divisible by 3
5560:
5 + 5 + 6 + 0 = 16
not divisible by 3
5568:
5 + 5 + 6 +8 = 24
divisible by 3, then 68 is an option
5576:
5 +5 + 7 + 6 = 23
not divisible by 3
5582:
5 +5 + 8 + 2 = 20
not divisible by 3
5590:
5 +5 +9 + 0 = 19
not divisible by 3
5598:
5 + 5 + 9 + 8 = 27
is divisible by 3, thus 98 is an option.
Then the possible options are:
98, 68, 44, 20