# XAT 2012 Quant Question 58 : LCM, Number Properties

## Question - 1 Mark

Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour 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 5

^{th} to January 28

^{th}, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the VPs?

- February 6, 2012
- February 7, 2012
- February 8, 2012
- February 9, 2012
- None of the above

**Correct Answer** : February 8, 2012. Choice (C)

#### Explanatory Answer

VP (HR) visits the plant every 3

^{rd} day (After a gap of 2 days. Please note carefully that the question states that the VP visisted after a gap of 2 days not every 2 days).

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 4

^{th} day (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 6

^{th} day (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 are 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.

Level of difficulty : Easy to Moderate

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