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20 Jan 2026, 03:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:23) correct
52%
(01:32)
wrong
based on 130
sessions
History
Date
Time
Result
Not Attempted Yet
Do at least 20 percent of Amity school students aspire to do masters in business management?
(1) In the school, the ratio of male students to female students is 5:7.
(2) In the school, of the total number of students, 30 percent of the male students and 22 percent of female students aspire to do the masters in business management.
(1) In the school, the ratio of male students to female students is 5:7.
(2) In the school, of the total number of students, 30 percent of the male students and 22 percent of female students aspire to do the masters in business management.
13 Feb 2026, 09:37
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We are asked:
Is at least 20% of the total student body aspiring to do a master’s in business management?
Statement (1) Alone
Male : Female = 5 : 7
This only tells us the gender split.
We are not told what percentage of either group aspires to do the master’s.
❌ Insufficient
Statement (2) Alone
30% of males aspire
22% of females aspire
But we do not know the male–female ratio, so we cannot compute the overall percentage.
Example:
If mostly males → overall > 20%
If mostly females → could be closer to 22%
Not enough information.
❌ Insufficient
Both Statements Together
Male : Female = 5 : 7
Let total students = 12 units
Males = 5
Females = 7
Now compute aspiring students:
From males:
0.30
×
5
=
1.5
0.30×5=1.5
From females:
0.22
×
7
=
1.54
0.22×7=1.54
Total aspiring:
1.5
+
1.54
=
3.04
1.5+1.54=3.04
Overall percentage:
3.04
12
=
0.2533
=
25.33
%
12
3.04
=0.2533=25.33%
This is greater than 20%.
The answer is definitively YES.
✅ Final Answer: C
Is at least 20% of the total student body aspiring to do a master’s in business management?
Statement (1) Alone
Male : Female = 5 : 7
This only tells us the gender split.
We are not told what percentage of either group aspires to do the master’s.
❌ Insufficient
Statement (2) Alone
30% of males aspire
22% of females aspire
But we do not know the male–female ratio, so we cannot compute the overall percentage.
Example:
If mostly males → overall > 20%
If mostly females → could be closer to 22%
Not enough information.
❌ Insufficient
Both Statements Together
Male : Female = 5 : 7
Let total students = 12 units
Males = 5
Females = 7
Now compute aspiring students:
From males:
0.30
×
5
=
1.5
0.30×5=1.5
From females:
0.22
×
7
=
1.54
0.22×7=1.54
Total aspiring:
1.5
+
1.54
=
3.04
1.5+1.54=3.04
Overall percentage:
3.04
12
=
0.2533
=
25.33
%
12
3.04
=0.2533=25.33%
This is greater than 20%.
The answer is definitively YES.
✅ Final Answer: C
13 Feb 2026, 13:10
Kudos
Bookmarks
This is a great overlapping sets problem that tests whether you can extract the specific group you need from ratio and percentage information.
**Understanding the question:** We need to know if ≥ 20% of total students aspire to do masters.
**Statement 1: Male to female ratio is 5:7.**
This tells us that out of every 12 students, 5 are male and 7 are female. But we have no information about who aspires to do masters. **Insufficient.**
**Statement 2: Of all students, 30% of males and 22% of females aspire to do masters.**
We know the percentages within each gender group, but we don't know the split between males and females in the school.
Let's test extremes:
- If the school is 100% male: 30% aspire (≥ 20%, answer is YES)
- If the school is 100% female: 22% aspire (≥ 20%, answer is YES)
- If the school is 50-50: 0.5(30%) + 0.5(22%) = 26% (≥ 20%, answer is YES)
Actually, any combination gives us ≥ 20% since both percentages are above 20%. Wait, let me verify this logic more carefully.
Actually, since both 30% and 22% are each individually ≥ 20%, any weighted average of these two will be ≥ 20%. **Sufficient.**
**Combined:** Not needed.
**Answer: B (Statement 2 alone is sufficient)**
**Common trap:** Thinking you need the ratio from Statement 1 to weight the percentages in Statement 2. But when both subgroup percentages exceed the threshold, you don't need to know the group sizes.
**Takeaway:** In overlapping sets, if all subgroups meet a threshold individually, the combined group automatically meets it too—no need to calculate the exact weighted average.
**Understanding the question:** We need to know if ≥ 20% of total students aspire to do masters.
**Statement 1: Male to female ratio is 5:7.**
This tells us that out of every 12 students, 5 are male and 7 are female. But we have no information about who aspires to do masters. **Insufficient.**
**Statement 2: Of all students, 30% of males and 22% of females aspire to do masters.**
We know the percentages within each gender group, but we don't know the split between males and females in the school.
Let's test extremes:
- If the school is 100% male: 30% aspire (≥ 20%, answer is YES)
- If the school is 100% female: 22% aspire (≥ 20%, answer is YES)
- If the school is 50-50: 0.5(30%) + 0.5(22%) = 26% (≥ 20%, answer is YES)
Actually, any combination gives us ≥ 20% since both percentages are above 20%. Wait, let me verify this logic more carefully.
Actually, since both 30% and 22% are each individually ≥ 20%, any weighted average of these two will be ≥ 20%. **Sufficient.**
**Combined:** Not needed.
**Answer: B (Statement 2 alone is sufficient)**
**Common trap:** Thinking you need the ratio from Statement 1 to weight the percentages in Statement 2. But when both subgroup percentages exceed the threshold, you don't need to know the group sizes.
**Takeaway:** In overlapping sets, if all subgroups meet a threshold individually, the combined group automatically meets it too—no need to calculate the exact weighted average.
