the number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the two digit number? List all options.

98, 68, 44, 20

Step-by-step 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

answer: the answer is e

step-by-step explanation: