Difference between revisions of "1955 AHSME Problems/Problem 37"

(Created page with "A three-digit number has, from left to right, the digits <math>h, t</math>, and <math>u</math>, with <math>h>u</math>. When the number with the digits reversed is subtracted f...")
 
(Solution)
 
Line 25: Line 25:
 
<cmath>  \text{5 9 4}</cmath>
 
<cmath>  \text{5 9 4}</cmath>
 
Out difference is <math>594</math>. Therefore, the next two digits, from right to left, are <math>\boxed{\textbf{(B) } \text{9 and 5}}</math>.
 
Out difference is <math>594</math>. Therefore, the next two digits, from right to left, are <math>\boxed{\textbf{(B) } \text{9 and 5}}</math>.
 +
 
==See Also==
 
==See Also==
 
Go to the rest of the [[1955 AHSME Problems]]
 
Go to the rest of the [[1955 AHSME Problems]]
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 14:34, 24 November 2020

A three-digit number has, from left to right, the digits $h, t$, and $u$, with $h>u$. When the number with the digits reversed is subtracted from the original number, the units' digit in the difference is 4. The next two digits, from right to left, are:

$\textbf{(A)}\ \text{5 and 9}\qquad\textbf{(B)}\ \text{9 and 5}\qquad\textbf{(C)}\ \text{impossible to tell}\qquad\textbf{(D)}\ \text{5 and 4}\qquad\textbf{(E)}\ \text{4 and 5}$

Solution

We can set up the subtraction like this: \[\text{ h t u}\] \[- \text{u t h}\] \[-------\] \[\text{? ? 4}\] Since $u < h$, we need to borrow the one from the tens column. Since the result of the tens column is 0, the taken 1 would result in the tens digit being 9:

\[\text{ h t u}\] \[- \text{u t h}\] \[-------\] \[\text{? 9 4}\] We can assign a value for $u$ and $h$, since that doesn't impact the difference, so lets say that $u=3$ and $h=9$. \[\text{ 9 t 3}\] \[- \text{3 t 9}\] \[-------\] \[\text{? 9 4}\] Since $t < t+1$, we can subtract one from the hundred's digit: \[\text{ 9 t 3}\] \[- \text{3 t 9}\] \[-------\] \[\text{5 9 4}\] Out difference is $594$. Therefore, the next two digits, from right to left, are $\boxed{\textbf{(B) } \text{9 and 5}}$.

See Also

Go to the rest of the 1955 AHSME Problems

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS