XAT 2012 Quant - Number Properties: LCM

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XAT 2012 Question 58  : LCM Word Problem

 Three Vice Presidents (VP) regularly visit the plant on different days. Due to labor unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5th to January  28th, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the VPs?
A.    February 6, 2012
B.    February 7, 2012
C.    February 8, 2012
D.    February 9, 2012
E.    None of the above

Correct Answer February 8, 2012.

Explanatory Answer

VP (HR) visits the plant every 3rd day (the question states the VP visits after a gap of 2 days). 

The most important point in this question is this point. As the VP visits the plant after a gap of 2 days - he visits the plant every third day - not every second day.


If VP (HR) visited the plant on day 0, he will visit again on day 3, day 6 and so on.
i.e., on days that are multiples of 3.

VP (Operations) visits the plant every 4th day (as he visits after a gap of 3 days).
If VP (Operations) visited the plant on day 0, he will visit again on day 4, day 8 and so on.
i.e., on days that are multiples of 4.

VP (Sales) visits the plant every 6th day (as the VP Sales visits after a gap of 5 days).
If VP (Sales) visited the plant on day 0, he will visit again on day 6, day 12 and so on.
i.e., on days that are multiples of 6.

So, all 3 VPs will visit the plant together again on a day that is a multiple of 3, 4 and 6 or on a day that is a common multiple of 3, 4 and 6.

The first such common multiple is the LCM of 3, 4 and 6 = 12.

The last date on which all three VPs met the CEO was on Jan 3, 2012.
The next dates on which their visits will coincide will be after 12 days and multiples therefore. 
i.e., on Jan 15, 2012, Jan 27, 2012, Feb 8, 2012.

The CEO is on leave from Jan 5, 2012 to Jan 28, 2012. 
So, the CEO will meet the VPs on February 8, 2012.