+0  
 
+1
54
4
avatar+44 

A digital, 12-hour clock shows hours and minutes. During what fraction of the day will the clock show the digit 1 in its display? Express your answer as a common fraction.

 

The correct answer is 1/2. But why?

CalculatorUser  Oct 14, 2018
 #1
avatar
0

In the 12 hours of AM, it will show for 1 full hour between 1 AM and 2 AM. So, that is: 1 in 12 hours.

In the 12 hours of  PM, it will show for 1 full hour between 1 PM and 2 PM. So, that is: 1 in 12 hours.

So: 1 + 1 =2 hours in 12 + 12 = 24 hours. Or 2 / 24 = 1 / 12, or 1 in 12 hours, not 1/2 as you have it written.

Note: I'm only counting the HOURS HAND!. The MINUTE HAND will show 16 ones EVERY HOUR!.

Guest Oct 14, 2018
edited by Guest  Oct 14, 2018
 #2
avatar
0

That cannot be right!! How about 10, 11, 12 O'clock.......etc.!!!!

Guest Oct 14, 2018
 #3
avatar+91112 
+2

There are  12 * 60   =  720  possible minutes displayed

 

From 10 - 2....  4hrs * 60 mintes per hour   = 240  minutes display  a "1"

 

Every hour between 2 and 10.....the following minutes display at least one "1"

 

10 , 11, 12, 13, 14, 15, 16 ,17 , 18, 19

01, 21, 31, 41, 51

 

So...that's  15 occurrences per hour  * 8 hrs  =  120 additional minutes

 

So...the total number of minutes displaying  at least one "1"  = 240 + 120  = 360

 

So

 

360 / 720    = 1/2    !!!

 

cool cool cool

CPhill  Oct 14, 2018
edited by CPhill  Oct 15, 2018
 #4
avatar+44 
+1

Thank you so much!!! I understand now!

CalculatorUser  Oct 14, 2018

16 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.