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In a group of 5 students, some study French

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In a group of 5 students, some study French [#permalink]

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In a group of 5 students, some study French, some study German, some study both. Two students are selected to be sent for a technical presentation having delegates from France as well as Germany. What could be the probability that lectures given by French as well as German delegates would be understood by the team of two students?
A)0.42
B)0.45
C)0.60
D)0.72
E)0.75

Source: Self-made
[Reveal] Spoiler: OA

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Last edited by gmatbusters on 01 Dec 2017, 17:48, edited 1 time in total.

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Re: In a group of 5 students, some study French [#permalink]

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New post 01 Dec 2017, 08:32
Isn't more information needed to solve this problem? Specifically either how many speak German or French or both?

Otherwise I'm stumped on how to get the answer.

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Re: In a group of 5 students, some study French [#permalink]

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New post 01 Dec 2017, 10:01
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Janvisahu wrote:
In a group of 5 students, some study French, some study German, some study both. Two students are selected to be sent for a technical presentation having delegates from France as well as Germany. Find the probability that lectures given by French as well as German delegates would be understood by the team of two students.
A)0.42
B)0.45
C)0.60
D)0.72
E)0.75

Source: Self-made


This can be solved only by back-solving.
Since 2 students to be selected who understand both French and German, minimum students who know both languages must be 2 otherwise probability would be zero, which is not in the options.
Prob that 2 students know both languages = 1/5 = 0.2 not an option.
Consider 3 students know both languages, prob =3/5 = 0.6.
Option C
Consider 4 students know both languages, prob =4/5 = 0.8, not an option.
Hence answer C.
However, this is not a GMAT type question.
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In a group of 5 students, some study French [#permalink]

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New post 01 Dec 2017, 16:49
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Hi souvonik2k, you have answered the question correctly kudos to you.
This question is based on a basic logic ,
I will describe my logic here.
We do not know the number of students studying French or how many of them study German, so it is not possible to find the number of favorable events that one of the students is French student, and other is German student. But we can always say for sure that the number of favorable events will be a positive integer.
Now the total number of events will be 5C2 = 5!/(3!2!) = 10.
Hence required probability = positive integer/ 10
which always gives a single decimal or an integer. So from the options given, only C has a single decimal, other choices have two decimal.
Hence, Clearly, C is the answer.

This concept will be very useful for the complex probability questions, If we know that denominator is 10, then probability can not have 2 digit decimal answer, or so on. No need to calculate the number of cases which is a very tiresome process for some complex problems.



souvonik2k, Bunuel, VeritasPrepKarishma , Now tell me is the question a good one for GMAT?

(PS - I saw a concept video for probability by some GMAT prep, which inspires me to make this question.)

Please give kudos :thumbup: , if you like my post
I believe in learning by doing... I will be posting questions based on the basic concepts, but tricky though :cool: :grin:

souvonik2k wrote:


Janvisahu wrote:
In a group of 5 students, some study French, some study German, some study both. Two students are selected to be sent for a technical presentation having delegates from France as well as Germany. Find the probability that lectures given by French as well as German delegates would be understood by the team of two students.
A)0.42
B)0.45
C)0.60
D)0.72
E)0.75

Source: Self-made


This can be solved only by back-solving.
Since 2 students to be selected who understand both French and German, minimum students who know both languages must be 2 otherwise probability would be zero, which is not in the options.
Prob that 2 students know both languages = 1/5 = 0.2 not an option.
Consider 3 students know both languages, prob =3/5 = 0.6.
Option C
Consider 4 students know both languages, prob =4/5 = 0.8, not an option.
Hence answer C.
However, this is not a GMAT type question.

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Last edited by gmatbusters on 01 Dec 2017, 19:20, edited 2 times in total.

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Re: In a group of 5 students, some study French [#permalink]

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New post 01 Dec 2017, 17:22
Janvisahu wrote:
In a group of 5 students, some study French, some study German, some study both. Two students are selected to be sent for a technical presentation having delegates from France as well as Germany. Find the probability that lectures given by French as well as German delegates would be understood by the team of two students.
A)0.42
B)0.45
C)0.60
D)0.72
E)0.75

Source: Self-made


Hi...

A Question should be solvable, it may be that the choices are helpful at times.
But if we are looking at a question that has no solution and is totally dependent on the choices, then the Question has a big question mark '?' on it.
When you say " what is the probability...?", It means the question has ONE answer, but in this case there could be different answers
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In a group of 5 students, some study French [#permalink]

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New post 01 Dec 2017, 17:47
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Dear Sir
I agree with you, but in many GMAT questions, we get more than one answer and we do mark the options provided by the question.
I have edited the question by " what could be the probability " :thumbup:

Actually, my purpose of posting the question was to put emphasis on the concept, "This concept will be very useful for the complex probability questions, If we know that denominator is 10, then probability can not have 2 digit decimal answer, or so on. No need to calculate the number of cases which is a very tiresome process for some complex problems."


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chetan2u wrote:
Janvisahu wrote:
In a group of 5 students, some study French, some study German, some study both. Two students are selected to be sent for a technical presentation having delegates from France as well as Germany. Find the probability that lectures given by French as well as German delegates would be understood by the team of two students.
A)0.42
B)0.45
C)0.60
D)0.72
E)0.75

Source: Self-made


Hi...

A Question should be solvable, it may be that the choices are helpful at times.
But if we are looking at a question that has no solution and is totally dependent on the choices, then the Question has a big question mark '?' on it.
When you say " what is the probability...?", It means the question has ONE answer, but in this case there could be different answers

_________________

If you like my post, encourage me by providing Kudos...
Happy Learning...

Kudos [?]: 23 [1], given: 24

In a group of 5 students, some study French   [#permalink] 01 Dec 2017, 17:47
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