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Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Is the probability of choosing a student in class X who has scored  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 48% (01:22) correct 52% (01:25) wrong based on 94 sessions

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Is the probability of choosing a student in class X who has scored more than 50% greater than $$\frac{1}{4}$$?

(1) probability of choosing a boy in class X who has scored more than 50% is $$\frac{1}{2}$$.
(2) probability of choosing a girl in the class X is $$\frac{2}{5}$$.

self made

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Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Is the probability of choosing a student in class X who has scored  [#permalink]

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chetan2u wrote:
Is the probability of choosing a student in class X who has scored more than 50% greater than $$\frac{1}{4}$$?

(1) probability of choosing a boy in class X who has scored more than 50% is $$\frac{1}{2}$$.
(2) probability of choosing a girl in the class X is $$\frac{2}{5}$$.

self made

so Q is :- P of picking a student scoring more than 50% >1/4??

lets see the statements

(1) probability of choosing a boy in class X who has scored more than 50% is $$\frac{1}{2}$$.
Tells us about boys. nothing about girls..
insuff

(2) probability of choosing a girl in the class X is $$\frac{2}{5}$$
again info only about girls but doesn't tell us that how many girls score >50%
insuff

Combined
Easy to chose E as the numbers of both not known..
But always solve -
statement II tells us that girls are $$\frac{2}{5}$$ , so boys are $$\frac{3}{5}$$
statement I tells us that 1/2 of boys scored more than 50%
so ATLEAST $$\frac{1}{2}*\frac{3}{5}=\frac{3}{10}$$ scored more than 50%, even if none of the girls scored above 50%
$$\frac{3}{10}>\frac{1}{4}$$, so ans is always YES
suff

C
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Intern  B
Joined: 01 Nov 2017
Posts: 11
Re: Is the probability of choosing a student in class X who has scored  [#permalink]

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Question: if we know, that the probability of picking a boy (=student) who is better that 50%, do we really have to know any more information about the rest to answer the question?
In my understanding, the rest consists of a. boys below 50%, b. girls above 50%, c. girls below 50% (consolidated = other 50% of total of students).
Therefor I know, that whatever comes in addition, we for sure have a probability of greater 50% (if we have at least 1 girl who is better than 50%), and the given information in 1) is sufficient to answer. Because at least half of the total students are boys better than 50%.

If this is not the case the question is probably missleading the way it's stated.

Let me know what you think.
Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Re: Is the probability of choosing a student in class X who has scored  [#permalink]

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Gregsterh wrote:
Question: if we know, that the probability of picking a boy (=student) who is better that 50%, do we really have to know any more information about the rest to answer the question?
In my understanding, the rest consists of a. boys below 50%, b. girls above 50%, c. girls below 50% (consolidated = other 50% of total of students).
Therefor I know, that whatever comes in addition, we for sure have a probability of greater 50% (if we have at least 1 girl who is better than 50%), and the given information in 1) is sufficient to answer. Because at least half of the total students are boys better than 50%.

If this is not the case the question is probably missleading the way it's stated.

Let me know what you think.

Hi..
Question is perfectly fine and means exactly what it is intended to..
You are taking students as only boys which is wrong.. students will consist of both boys and girls.

The main statement tells us - Do 1/4 or 25% of students have got more than 50% marks..
1) statement I tells us that 50% of boys have got more than 50% marks..
If boys are 2 and girls 40.. boys Both >50% and 2 girls >50%.. overall 4 out of 42 students>50% , so ans is NO
If there are 40 boys and 10 girls, Ans is always YES
Insufficient

Hope it helps
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Joined: 13 Mar 2017
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Is the probability of choosing a student in class X who has scored  [#permalink]

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chetan2u wrote:
Gregsterh wrote:
Question: if we know, that the probability of picking a boy (=student) who is better that 50%, do we really have to know any more information about the rest to answer the question?
In my understanding, the rest consists of a. boys below 50%, b. girls above 50%, c. girls below 50% (consolidated = other 50% of total of students).
Therefor I know, that whatever comes in addition, we for sure have a probability of greater 50% (if we have at least 1 girl who is better than 50%), and the given information in 1) is sufficient to answer. Because at least half of the total students are boys better than 50%.

If this is not the case the question is probably missleading the way it's stated.

Let me know what you think.

Hi..
Question is perfectly fine and means exactly what it is intended to..
You are taking students as only boys which is wrong.. students will consist of both boys and girls.

The main statement tells us - Do 1/4 or 25% of students have got more than 50% marks..
1) statement I tells us that 50% of boys have got more than 50% marks..
If boys are 2 and girls 40.. boys Both >50% and 2 girls >50%.. overall 4 out of 42 students>50% , so ans is NO
If there are 40 boys and 10 girls, Ans is always YES
Insufficient

Hope it helps

I hope I will not see such a question on the real exam, as I understood the statement #1 exactly as Gregsterh did: the probability of choosing a student who is a boy AND also got more than 50% is 1/2. In that case statement#1 alone is sufficient indeed.
Intern  B
Joined: 02 May 2019
Posts: 19
Re: Is the probability of choosing a student in class X who has scored  [#permalink]

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Alisha1810 wrote:
chetan2u wrote:
Gregsterh wrote:
Question: if we know, that the probability of picking a boy (=student) who is better that 50%, do we really have to know any more information about the rest to answer the question?
In my understanding, the rest consists of a. boys below 50%, b. girls above 50%, c. girls below 50% (consolidated = other 50% of total of students).
Therefor I know, that whatever comes in addition, we for sure have a probability of greater 50% (if we have at least 1 girl who is better than 50%), and the given information in 1) is sufficient to answer. Because at least half of the total students are boys better than 50%.

If this is not the case the question is probably missleading the way it's stated.

Let me know what you think.

Hi..
Question is perfectly fine and means exactly what it is intended to..
You are taking students as only boys which is wrong.. students will consist of both boys and girls.

The main statement tells us - Do 1/4 or 25% of students have got more than 50% marks..
1) statement I tells us that 50% of boys have got more than 50% marks..
If boys are 2 and girls 40.. boys Both >50% and 2 girls >50%.. overall 4 out of 42 students>50% , so ans is NO
If there are 40 boys and 10 girls, Ans is always YES
Insufficient

Hope it helps

I hope I will not see such a question on the real exam, as I understood the statement #1 exactly as Gregsterh did: the probability of choosing a student who is a boy AND also got more than 50% is 1/2. In that case statement#1 alone is sufficient indeed.

I agree the wording to the first stem is off-putting. It should be along the lines of 1/2 of all the boys in class x scored greater than 50 percent. Especially for non-natives it would be easy to confuse the stem and 1/2 of the class is boys who scored greater than 50 percent. Re: Is the probability of choosing a student in class X who has scored   [#permalink] 06 Aug 2019, 07:26
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