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07 May 2018, 02:36
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:03) correct
25%
(01:18)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
A group of 9 teachers from the same middle school went to a teachers’ convention and split up into two groups to attend two different workshops. What percent of the 9 teachers were math teachers?
(1) Two math teachers from the group attended the workshop on fractions.
(2) Seven teachers from the group attended the workshop on classroom management.
(1) Two math teachers from the group attended the workshop on fractions.
(2) Seven teachers from the group attended the workshop on classroom management.
07 May 2018, 03:26
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Solution
Given:
• A group of 9 teachers from the same middle school attended the convention, in two groups
To find:
• What percent of the 9 teachers attended were math teachers
Analysing Statement 1
• As per the information given in Statement 1, two maths teachers from the group attended the workshop on fractions
- o From this, we cannot find out the exact number of maths teachers in the whole group of 9 teachers
Analysing Statement 2
• As per the information given in Statement 2, seven teachers from the group attended the workshop on classroom management
- o From this, we don’t get any information about the number of math teachers
Combining Both Statements
• Considering both statements together we can say:
- o 2 maths teachers attended the workshop on fraction
- o 7 teachers attended the workshop on classroom management
• Therefore, we cannot find out the exact number of maths teachers
Hence, the correct answer is Option E.
Answer: E
20 Jun 2019, 02:57
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This is a simple, but tricky question on percentages. To be able to calculate the required percentage, we need to know the exact number of math teachers in the school.
So, any data that gives us this exact number will be sufficient data.
From statement I alone, we know for sure about the 2 math teachers who attended the fractions workshop. But, there may have been some math teachers who attended the other workshop (whatever that may be). We don’t have data about this part.
If we have only 2 math teachers, the percentage will be \(\frac{2}{9}\) or 22.22%.
If all the other teachers who attended the other workshop are also math teachers, the percentage becomes 100%.
This means, the required percentage is a range and not a single value.
So, statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we know seven teachers attended the classroom management workshop. However, we do not know how many of these were math teachers.
Additionally, we do not have any information about the other two teachers.
If the other two teachers are math teachers and the seven are not, the percentage of math teachers will be \(\frac{2}{9}\) i.e 22.22%.
If the other two teachers are not math teachers and the seven teachers are also not math teachers, the percentage could be 0%.
Here again, we see that it’s a range. Statement II alone is insufficient. Answer options B can be eliminated.
On combining the two statements, we still do not have information about how many of the seven teachers are math teachers. So, the percentage of math teachers will still stay between 22.22% and 100%.
Answer option C can be eliminated. The correct answer option is E.
Because two and seven add up to 9, which is the total number of teachers, it is not necessary that they are mutually exclusive groups. But, it’s very hard to resist the temptation of assuming so. This is the trap in this question that you will have to avoid falling into.
Hope this helps!
So, any data that gives us this exact number will be sufficient data.
From statement I alone, we know for sure about the 2 math teachers who attended the fractions workshop. But, there may have been some math teachers who attended the other workshop (whatever that may be). We don’t have data about this part.
If we have only 2 math teachers, the percentage will be \(\frac{2}{9}\) or 22.22%.
If all the other teachers who attended the other workshop are also math teachers, the percentage becomes 100%.
This means, the required percentage is a range and not a single value.
So, statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we know seven teachers attended the classroom management workshop. However, we do not know how many of these were math teachers.
Additionally, we do not have any information about the other two teachers.
If the other two teachers are math teachers and the seven are not, the percentage of math teachers will be \(\frac{2}{9}\) i.e 22.22%.
If the other two teachers are not math teachers and the seven teachers are also not math teachers, the percentage could be 0%.
Here again, we see that it’s a range. Statement II alone is insufficient. Answer options B can be eliminated.
On combining the two statements, we still do not have information about how many of the seven teachers are math teachers. So, the percentage of math teachers will still stay between 22.22% and 100%.
Answer option C can be eliminated. The correct answer option is E.
Because two and seven add up to 9, which is the total number of teachers, it is not necessary that they are mutually exclusive groups. But, it’s very hard to resist the temptation of assuming so. This is the trap in this question that you will have to avoid falling into.
Hope this helps!
