An automated answering machine checks for missed calls every three minutes and voice messages every seven minutes. It beeps every time when both are done at the same time. How many times it will beep during 45 minutes duration?
Please attempt the above question timed, and then click below to reveal the few second technique leading to the correct answer

Hours:Minutes:Seconds

00:00:00

Technique:

Step 1. First, list all the multiples of the higher number of minutes, which is 7 up to 45 7, 14, 21, 28, 35, 42

Step 2. Now, without listing the multiples of the lower number of minutes which is 3, mentally check whether any of the numbers listed in step 1 is / are a multiple of the lower number of minutes which is 3. In other words, you go through the times table of 3 very quickly up to the last number in step1 which is 42. You now got only two numbers which are 21 and 42.
Therefore the answer is : 2

Answer:2 times

Time allowed: 30 seconds

Time taken using the technique: 3 seconds

Time saved = 27 seconds [9/10 ^{th} of time allowed by examiner]

NOTE : Most students will list the multiples of both numbers, i.e. 3 and 7 minutes and look for common numbers comparing the two listings consuming either the total time allowed or exceeding the time allowed. If the child is very fluent with the times table, answering this question can be further shortened.

WORK SHEET – Practice question

An automated answering machine checks for missed calls every four minutes and voice messages every six minutes. It beeps every time when both are done at the same time. How many times it will beep during 30 minutes duration?