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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, 09:26
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Difficulty:

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Question Stats:

58% (02:00) correct 42% (01:55) wrong based on 98 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 Jul 2019, 07:56
1
Tim's houses are numbers : 10,20,30,40,50,........
Jack's houses are numbers : 6,12,18,24,30,36,..........

the first common number between the two sequences is 30 ----> this is a
and the LCM between 10 (2*5 of Tim) and 6 (2*3 of jack) is 30 ---> this is d
the last number in the sequence is 150 ---> Sn

so the new common sequence between them is:
a,a+d,a+2d,......
30,60,90,120,150 (5 members) ---> this is n

algebraically:
n = (Sn-a)/d + 1

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

D
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Originally posted by Mahmoudfawzy83 on 23 Jan 2019, 09:45.
Last edited by Mahmoudfawzy83 on 23 Jul 2019, 07:56, edited 2 times 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, 10:04
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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, 10:06
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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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,  [#permalink]

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New post 23 Jan 2019, 10:22
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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]

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New post 29 Jul 2019, 07:40
Bunuel, a little help here, please?
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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 03 Aug 2019, 21:40
KanishkM wrote:
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


I found that the question misses the word "both". It says "to protect each house whose number is a multiple of 2 and 5" - I interpreted it as protect a house which is a multiple of 2 & also protect a house which is a multiple of 5. Had the question said ""to protect each house whose number is a multiple of (both) 2 and 5", I would have agreed to the answer.

Please guide me on why my interpretation was wrong as per OA
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Re: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John,   [#permalink] 03 Aug 2019, 21:40
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