SOLUTION: In multiplying two positive integers a and b, Joey inadvertently reversed the digits of the two-digit number a. His erroneous product was 161. What is the value of (ab)^2?

Algebra ->  Test  -> Lessons -> SOLUTION: In multiplying two positive integers a and b, Joey inadvertently reversed the digits of the two-digit number a. His erroneous product was 161. What is the value of (ab)^2?      Log On


   

Question 704229: In multiplying two positive integers a and b, Joey inadvertently reversed the digits of the two-digit number a. His erroneous product was 161. What is the value of (ab)^2?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
In multiplying two positive integers a and b, Joey inadvertently reversed the digits of the two-digit number a. His erroneous product was 161. What is the value of (ab)^2?
------------------------------
By dividing 161 by odd prime numbers, trying to find one that
will give a whole number, when we come to dividing 161 by 7 
we get the integer 23.  So

161 = 7×23

So the two-digit number "a" with the digits reversed was 23,


Therefore a = 32, and b = 7.

So (ab)² = (32×7)² = 224² = 50176

Edwin