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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 2-digit number? List all options.

Sagot :

Given:

The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.

To find:

The 2-digit numbers.

Solution:

Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].

We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.

Now,

[tex]5500=229\times 24+4[/tex]

It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:

[tex]5496+24=5520[/tex]

[tex]5520+24=5544[/tex]

[tex]5544+24=5568[/tex]

[tex]5568+24=5592[/tex]

Therefore, the possible 2-digit numbers are 20, 44, 68, 92.

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