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Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $1−A−2−. What is the missing digit A of this 3-digit number?


I dont get it

Sagot :

The missing digit is represented by A  ⇒  $1A2, where A represents a whole number from 0 to 9.

Try substituting any number from 0 to 9 for A (the middle digit or tens place) , then divide by 11 members.

Option 1:  A = 2  ⇒ $1 2 2
$122 ÷ 11 = $11.09090909...

Option 2:  A = 3  ⇒  $1 3 2
$ 132 ÷ 11 = $12

Option 3:  A = 9   ⇒     $ 1 9 2
$ 192 ÷ 11 = $ 17,45454545,,,

When you substitute the rest of the one-digit number for A, the decimals are repeating.  (Amazing, right? Try it)

The only one-digit that gives a whole number quotient when it takes the place of tens digit in $1 __2  is 3.   Because $ 132 ÷ 11 = $ 12. (Option 2)

The missing digit is 3.