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On Christmas, a class teacher gave a gift pack to each student present

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Joined: 30 Aug 2017
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On Christmas, a class teacher gave a gift pack to each student present [#permalink]

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New post 19 Oct 2017, 08:51
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Question Stats:

53% (01:08) correct 47% (00:53) wrong based on 73 sessions

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On Christmas, a class teacher gave a gift pack to each student present in a class. Each pack had x chocolates, y biscuits and z toffees. How many students were there in the class?

(1) Each student received chocolates, biscuits and toffees in the ratio 1:2:4.

(2) The class teacher distributed a total of 7 chocolates, 14 biscuits and 28 toffees and the number of students present in the class was more than 1.
[Reveal] Spoiler: OA
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Re: On Christmas, a class teacher gave a gift pack to each student present [#permalink]

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New post 19 Oct 2017, 09:17
A little confused on why this is B. Can you please elaborate?
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On Christmas, a class teacher gave a gift pack to each student present [#permalink]

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New post 19 Oct 2017, 09:42
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mcm2112 wrote:
A little confused on why this is B. Can you please elaborate?



Let total number of students be N.
⇒ Total number of chocolates, biscuits and toffees distributed by teacher will be Nx, Ny and Nz, respectively.

Considering statement 1:
Each student received chocolates, biscuits and toffees in the ratio 1 : 2 : 4.
⇒ y = 2x and z = 4x
i.e. total number of chocolates, biscuits and toffees distributed by teacher will be Nx, 2Nx and 4Nx respectively.

From above statement, it is impossible to determine the definite value of number of students present in the class.

Since we are not getting a definite answer from above statement, statement 1 itself is not sufficient to provide the answer.

Considering statement 2:
The class teacher distributed a total of 7 chocolates, 14 biscuits and 28 toffees and the number of students present in the class was more than 1.

⇒ Nx = 7, Ny = 14, and Nz = 28
Also N > 1

From the equation Nx = 7, it can be concluded that N is a factor of 7. Hence, the only value possible for N is 7 itself, as N > 1.

Since we are getting a definite answer from above statement, statement 2 itself is sufficient to provide the answer.

Answer: B. ------ IMO

Anyone can find any error and please let us know.

Hope that helps
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Re: On Christmas, a class teacher gave a gift pack to each student present [#permalink]

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New post 19 Dec 2017, 13:49
This question is a piece of cake if you read the stems carefully:

Question: Number of students.
Info: Ratios of Chocolate (x), (y) biscuits and (z) toffees.

1) Ratios => without total Numbers is useless.
Not Sufficient.

2) The class teacher distributed a total of 7 chocolates, 14 biscuits and 28 toffees and the number of students present in the class was more than 1.

First to notice, we got the total of chocolates, as chocolates are units that can't be dividided and 7 is prime number, this piece of information is very valuable, because the choices so far are 1 and 7 for the number of students. Then we know there are more than one Student. Only possible choice is 7.
Re: On Christmas, a class teacher gave a gift pack to each student present   [#permalink] 19 Dec 2017, 13:49
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On Christmas, a class teacher gave a gift pack to each student present

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