Question

Mary thought of a positive two-digit number. She multiplied it by $3$ and added $11.$ Then she switched the digits of the result, obtaining a number between $71$ and $75,$ inclusive. What was Mary's number?

$11$

$12$

$13$

$14$

$15$

Solution:

We know that her number was between $71$ and $75,$ so the units digit is between $1$ and $5,$ and the tens digit is $7.$

Now, we have to reverse the order of the operations. After reversing, we get the tens digit to be between $1$ and $5$ and the units digit to be $7.$

Then, subtracting $11$ subtracts $1$ from the units digit and the tens digit, giving us a number where the tens digit is between $0$ and $4$ and the units digit is $6.$ This must be a multiple of $3,$ so we can only have $36.$ Dividing this by $3$ yields $12.$

Thus, the correct answer is B .

2017 AMC 10B Problem 1

Solution:

Problem 1 in Other Years