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A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,

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A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post 23 Jan 2019, 08:26
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Difficulty:

  45% (medium)

Question Stats:

53% (01:48) correct 47% (01:35) wrong based on 40 sessions

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A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John, were appointed by the colony in charge. Tim was to protect each house whose number is a multiple of 2 and 5, Jack was to protect each house whose number is a multiple of 2 and 3 whereas John was asked to protect rest of the houses. How many houses were to be protected by both Tim& Jack?

A. 2
B. 3
C. 4
D. 5
E. More than 5
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A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post Updated on: 23 Jan 2019, 09:18
to be guarded by both Tim and Jack, the house's number must be a multiple of 2,3,5 = 30

number of houses = \(\frac{[150-30]}{30} + 1 = 5\)

D
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Originally posted by Mahmoudfawzy83 on 23 Jan 2019, 08:45.
Last edited by Mahmoudfawzy83 on 23 Jan 2019, 09:18, edited 1 time in total.
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post 23 Jan 2019, 09:04
1
akurathi12 wrote:
A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John, were appointed by the colony in charge. Tim was to protect each house whose number is a multiple of 2 and 5, Jack was to protect each house whose number is a multiple of 2 and 3 whereas John was asked to protect rest of the houses. How many houses were to be protected by both Tim& Jack?

A. 2
B. 3
C. 4
D. 5
E. More than 5


Houses numbered from 1 to 150, out of which

Tim was to protect each house whose number is a multiple of 2 and 5

Jack was to protect each house whose number is a multiple of 2 and 3

This means we can divide 150/15 to get the number of houses which will have numbers with multiple of 15(LCM of 3 and 5) .

Now we can divide this by 10/2 to get the number of houses which will be common to them

Answer D
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post 23 Jan 2019, 09:06
Mahmoudfawzy83 wrote:
to be guarded by both Tim and Jack, the house's number must be a multiple of 2,3,5 = 30

number of houses = \(\frac{150}{30} + 1 = 5\)

D


Will that be not 6 ??

Do let me know if i am incorrect.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post 23 Jan 2019, 09:22
1
KanishkM wrote:
Mahmoudfawzy83 wrote:
to be guarded by both Tim and Jack, the house's number must be a multiple of 2,3,5 = 30

number of houses = \(\frac{150}{30} + 1 = 5\)

D


Will that be not 6 ??

Do let me know if i am incorrect.


Thanks, I had a typo
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,   [#permalink] 23 Jan 2019, 09:22
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A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,

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