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A colony has houses numbered 1 to 150. Three guards, Tim, Jack and Joh
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13 Jul 2023, 06:13
13 Jul 2023, 06:13
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65% (02:15) correct
34% (02:09) wrong based on 23 sessions
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A colony has houses numbered 1 to 150. Three guards, Tim, Jack and John, were appointed by the colony in charge. Tim was to guard each house whose number is a multiple of 2 and 5 and Jack was to guard each house whose number is a multiple of 2 and 3 whereas John was asked to guard rest of the houses. How many houses are guarded by both Tim and Jack?
A. 2
B. 3
C. 4
D. 5
More than 5
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A. 2
B. 3
C. 4
D. 5
More than 5
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack and Joh
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14 Jul 2023, 13:07
14 Jul 2023, 13:07
1
Expert Reply
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.
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.
Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack and Joh
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07 Sep 2023, 17:43
07 Sep 2023, 17:43
2
A more condensed solution than the one offered above is this: Houses guarded by Tim and Jack are multiples of 2, 3, and 5. The LCM of 2, 3, and 5 is 30. 150/30 is 5. D is the answer.
