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21 Apr 2026, 03:12
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Column A: 6n/7
Column B: 11n/14
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
67% (01:21) correct
33%
(01:34)
wrong
based on 3
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Two-Part Analysis - Math/Hard
At a museum, n visitors were asked whether they wanted two optional add-ons for their ticket: an audio guide and rooftop access. Each visitor gave a yes-or-no answer for each add-on.
3/7 of the visitors said yes to the audio guide. Of those visitors, 1/3 also said yes to rooftop access. Among the visitors who said no to the audio guide, 5/8 said yes to rooftop access.
Select for Column A the expression that represents the number of visitors who did not say yes to both add-ons, and select for Column B the expression that represents the number of visitors who did not say no to both add-ons. Make only two selections, one in each column.
| Column A | Column B | |
| n/7 | ||
| 3n/14 | ||
| 5n/14 | ||
| 4n/7 | ||
| 11n/14 | ||
| 6n/7 |
ShowHide Answer
Official Answer
Column A: 6n/7
Column B: 11n/14
21 Apr 2026, 03:27
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Bunuel
Column A
We want the number of visitors who did not say yes to both add-ons. So first find the number who did say yes to both.
The number who said yes to the audio guide is 3n/7
Of those, the number who also said yes to rooftop access is 1/3 * 3n/7 = n/7
So n/7 visitors said yes to both add-ons.
Therefore, the number who did not say yes to both add-ons is
n - n/7 = 6n/7
Column B
We want the number of visitors who did not say no to both add-ons. So first find the number who did say no to both.
The number who said no to the audio guide is n - 3n/7 = 4n/7
Of those, the number who said yes to rooftop access is 5/8 * 4n/7 = 5n/14
So among the visitors who said no to the audio guide, the number who also said no to rooftop access is
4n/7 - 5n/14 =
= 8n/14 - 5n/14 =
= 3n/14
So 3n/14 visitors said no to both add-ons.
Therefore, the number who did not say no to both add-ons is
n - 3n/14 = 11n/14
Correct selections:
Column A: 6n/7
Column B: 11n/14
Takeaway
In group-counting questions built around two yes/no categories, the key is to identify the complement of the group named in the question and determine exactly which cases must be excluded to get the required count. To do this correctly, track the groups carefully at each step and keep clear which fraction is being applied to which subgroup.
What This Question Tests
This is a math-based two-part analysis question testing group breakdowns, conditional fractions, complementary counting, and overlap logic. It tests whether you can translate verbal conditions into exact subgroup counts while keeping the base group for each fraction clear.
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