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­A group of friends decides to travel to a neighbouring island for the

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chetan2u
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­A group of friends decides to travel to a neighbouring island for the [#permalink] New post   15 Feb 2024, 06:22
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Data Insights (DI) Butler 2024 [ Date: 15-Feb-2023] 



­A group of friends decides to travel to a neighbouring island for their summer vacation. However, the group is divided on the mode of transport to be used. Exactly two-fifth of the group wants to travel by ship, while exactly one-third of the group would prefer air travel.

In the table below, select for x the minimum possible number of the friends in the group and select for y the option that cannot be the number of friends in the group.­­­
x y
15
25
30
45
75
105
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Re: ­A group of friends decides to travel to a neighbouring island for the [#permalink] New post   26 Feb 2024, 03:06
chetan2u plz post the solution
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­A group of friends decides to travel to a neighbouring island for the [#permalink] New post   26 Feb 2024, 06:47
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Let there be z number of people in the group.
1) exactly 2z/5 want to travel by ship.
2) exactly z/3 want to travel by aircraft.

Since, we are talking of number of people in above two cases, both 2z/5 and z/3 must be integers. Thus, z must be a multiple of 5 and 3 or z is surely a multiple of 15.

The minimum value of z, that is x, is 15 itself.
The option that cannot be a value of z: All multiples of 15 are possible values of z. Only 25 in the option is not a multiple of 15. Thus y is 25.

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Re: ­A group of friends decides to travel to a neighbouring island for the [#permalink] New post   06 Mar 2024, 17:49
chetan2u wrote:
Data Insights (DI) Butler 2024 [ Date: 15-Feb-2023] 



­A group of friends decides to travel to a neighbouring island for their summer vacation. However, the group is divided on the mode of transport to be used. Exactly two-fifth of the group wants to travel by ship, while exactly one-third of the group would prefer air travel.

In the table below, select for x the minimum possible number of the friends in the group and select for y the option that cannot be the number of friends in the group.­­­


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Re: ­A group of friends decides to travel to a neighbouring island for the [#permalink] New post   29 Mar 2024, 14:27
Ship: 2/5
Air: 1/3

The number of friends should be divisible by 15 (=3*5)

=> Minimum (x): 15

=> Impossible option (y): 25
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Re: ­A group of friends decides to travel to a neighbouring island for the [#permalink]
29 Mar 2024, 14:27
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