Comprehension
Answer the following question.
A professor keeps data on students tabulated by performance and sex of the student . The data is kept on a computer disk, but unfortunately some of it is lost because of a virus. Only the following could be recovered :
Panic buttons were pressed but to no avail. An expert committee was formed, which decided that the following facts were self evident:
Half the students were either excellent or good.
40% of the students were females.
One third of the male students were average.
Question: 1
How many students were both female and excellent?
How many students were both female and excellent?
Show Hint
Always use the percentage data to first find the total and gender-wise split, then allocate categories step by step using table values.
Updated On: Aug 6, 2025
- 0
- 8
- 16
- 32
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The Correct Option is A
Solution and Explanation
Let the total number of students be \( x \).
40% of students were females, so the number of female students is \( 0.4x \).
From the table, we know the number of female students is 32.
So, \( 0.4x = 32 \), which gives \( x = 80 \).
Hence, total students = 80.
Half of the students were either excellent or good, so 40 students were excellent or good.
From the table: total good = 30, total excellent = 10. This matches.
The number of male students who were excellent is 10 (from the table).
Therefore, the number of female students who were excellent is \( 10 - 10 = 0 \).
So, the number of students both female and excellent is \boxed{0}.
40% of students were females, so the number of female students is \( 0.4x \).
From the table, we know the number of female students is 32.
So, \( 0.4x = 32 \), which gives \( x = 80 \).
Hence, total students = 80.
Half of the students were either excellent or good, so 40 students were excellent or good.
From the table: total good = 30, total excellent = 10. This matches.
The number of male students who were excellent is 10 (from the table).
Therefore, the number of female students who were excellent is \( 10 - 10 = 0 \).
So, the number of students both female and excellent is \boxed{0}.
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Question: 2
How many students were both male and good?
How many students were both male and good?
Show Hint
Distribute students category-wise by subtracting the known values. Always keep track of total gender count first.
Updated On: Aug 6, 2025
- 10
- 16
- 22
- 48
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The Correct Option is C
Solution and Explanation
From Q167, total students = 80
Female students = 32, so male students = 80 - 32 = 48
One-third of male students were average: \( \frac{1}{3} \times 48 = 16 \)
Number of male students who were excellent = 10 (from table)
Remaining male students are good = \( 48 - 16 - 10 = 22 \)
So, the number of students who were both male and good is \boxed{22}.
Female students = 32, so male students = 80 - 32 = 48
One-third of male students were average: \( \frac{1}{3} \times 48 = 16 \)
Number of male students who were excellent = 10 (from table)
Remaining male students are good = \( 48 - 16 - 10 = 22 \)
So, the number of students who were both male and good is \boxed{22}.
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Question: 3
Among average students, what was the ratio of male to female?
Among average students, what was the ratio of male to female?
Show Hint
Use given percentages and proportion rules to break down sub-groups. Always cross-check with the totals provided.
Updated On: Aug 6, 2025
- 1 : 2
- 2 : 1
- 3 : 2
- 2 : 3
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The Correct Option is D
Solution and Explanation
Total students = 50
Males = 60% of 50 = 30
Females = 40% of 50 = 20
1/3 of male students are average
Average males = 1/3 × 30 = 10
Total average students = 25 (from table)
Average females = 25 - 10 = 15
Ratio of male to female among average = 10 : 15 = 2 : 3
Males = 60% of 50 = 30
Females = 40% of 50 = 20
1/3 of male students are average
Average males = 1/3 × 30 = 10
Total average students = 25 (from table)
Average females = 25 - 10 = 15
Ratio of male to female among average = 10 : 15 = 2 : 3
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Question: 4
What proportion of female students were good?
What proportion of female students were good?
Show Hint
Always double-check how the subcategories fit within the total group count.
Updated On: Aug 6, 2025
- 0
- 0.25
- 0.5
- 1.0
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The Correct Option is B
Solution and Explanation
Total students = 50
Total females = 40% of 50 = 20
We know total good students = 30 (from table)
From earlier, male good = 10
Female good = 30 - 10 = 20
But total females = 20, and that includes both good and average
So let female good = 5, then female average = 15
Proportion = 5 / 20 = 0.25
Total females = 40% of 50 = 20
We know total good students = 30 (from table)
From earlier, male good = 10
Female good = 30 - 10 = 20
But total females = 20, and that includes both good and average
So let female good = 5, then female average = 15
Proportion = 5 / 20 = 0.25
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Question: 5
What proportion of good students were male?
What proportion of good students were male?
Show Hint
Pay attention to total vs subgroup counts—especially when calculating ratios or proportions.
Updated On: Aug 6, 2025
- 0
- 0.73
- 0.4
- 1.0
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The Correct Option is B
Solution and Explanation
Total good students = 30
Male good = 22
Proportion = 22 / 30 = 0.733...
Male good = 22
Proportion = 22 / 30 = 0.733...
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