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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack and Joh [#permalink]
GeminiHeat wrote:
To determine the number of houses guarded by both Tim and Jack, we need to identify the houses that are multiples of both 2 and 5, as well as multiples of both 2 and 3.

First, let's identify the houses Tim guards. Tim guards houses that are multiples of 2 and 5. We can find these houses by finding the multiples of their least common multiple (LCM), which is 10. The houses guarded by Tim are 10, 20, 30, ..., 150.

Next, let's identify the houses Jack guards. Jack guards houses that are multiples of 2 and 3. We can find these houses by finding the multiples of their LCM, which is 6. The houses guarded by Jack are 6, 12, 18, ..., 150.

To find the houses guarded by both Tim and Jack, we need to find the common multiples of 10 and 6 within the range of 1 to 150.

The multiples of 10 within this range are: 10, 20, 30, 40, 50, ..., 150.
The multiples of 6 within this range are: 6, 12, 18, 24, ..., 150.

By comparing these two lists, we can see that the common multiples are: 12, 30, 60, 90, and 150.

Therefore, there are 5 houses that are guarded by both Tim and Jack.

The correct answer is (D) 5.


12?? And also, don't you think that questions should say that Tim is in charge of the houses, which are multiples of 2 and 5 BOTH or something like a common multiple? In the GRE, grammar is important, I think.
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack and Joh [#permalink]
there's a really good free "cheat sheet" pdf download re. HCF and LCM on Ultimate Tuition's GRE page... I'd also look at that
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