2011 AMC 10B Problem 5

Question

In multiplying two positive integers

a

and

b,

Ron reversed the digits of the two-digit number

a.

His erroneous product was

161.

What is the correct value of the product of

a

and

b?

116

161

204

214

224

Factor

161

The only two-digit factor tells you the reversed value of

a

The number

161

is equal to

7\cdot 23.

There are no other pairs of numbers that multiply to

161

besides

1\cdot 161,

so

23

is the only two digit factor. Thus,

23

is the number reversed, so he meant to get

32\cdot 7

which is

224.

Thus, the correct answer is E .

Problem 5 in other years