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Originally posted by Bunuel on 29 Aug 2026, 11:55.
Last edited by Bunuel on 29 Aug 2026, 11:55, edited 1 time in total.
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Dropdown 1: 80
Dropdown 2: 90
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Difficulty:
95%
(hard)
Question Stats:
52%
(03:10)
correct 48%
(03:43)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
The diagram above summarizes Elena’s assessment of all customer complaints received by a retailer during one month. Elena classifies each complaint as involving at least one of three issues: billing, delivery, or product quality. The percentage shown in each region represents the percentage of all complaints that Elena classifies as involving the issue or combination of issues represented by that region.
Marcus, another quality analyst, agrees with much of Elena’s assessment. In particular:
• Whenever Elena says that a complaint involves billing, Marcus agrees that it involves billing. • Whenever Elena says that a complaint involves delivery, Marcus agrees that it involves delivery. • Whenever Elena says that a complaint involves product quality, Marcus agrees that it involves product quality.
However, Marcus differs from Elena in one respect: he believes that every complaint involving product quality also involves delivery. Apart from this difference, his assessment is the same as Elena’s.
Select from each drop-down menu the option that completes the statement most accurately based on the information provided.
Marcus maintains that % of the complaints involving billing also involve delivery.
Marcus maintains that % of all complaints involve delivery.
The diagram above summarizes Elena’s assessment of all customer complaints received by a retailer during one month. Elena classifies each complaint as involving at least one of three issues: billing, delivery, or product quality. The percentage shown in each region represents the percentage of all complaints that Elena classifies as involving the issue or combination of issues represented by that region.
Marcus, another quality analyst, agrees with much of Elena’s assessment. In particular:
• Whenever Elena says that a complaint involves billing, Marcus agrees that it involves billing. • Whenever Elena says that a complaint involves delivery, Marcus agrees that it involves delivery. • Whenever Elena says that a complaint involves product quality, Marcus agrees that it involves product quality.
However, Marcus differs from Elena in one respect: he believes that every complaint involving product quality also involves delivery. Apart from this difference, his assessment is the same as Elena’s.
Select from each drop-down menu the option that completes the statement most accurately based on the information provided.
Marcus maintains that % of the complaints involving billing also involve delivery.
Marcus maintains that % of all complaints involve delivery.
Official Solution:
Marcus keeps all of the issues that Elena assigns to each complaint. His only disagreement is that he believes every complaint involving product quality also involves delivery.
Therefore, Marcus adds delivery to two groups in Elena’s diagram:
• Product quality only, 5%, becomes product quality and delivery. • Billing and product quality only, 8%, becomes billing, product quality, and delivery.
Drop-down 1:
According to Elena’s diagram, the complaints involving billing are:
10% + 20% + 8% + 12% = 50%
Marcus agrees that all of these complaints involve billing.
Of these billing complaints, the ones Marcus says also involve delivery are:
20% + 8% + 12% = 40%
The 8% is included because these complaints involve product quality, and Marcus believes that every complaint involving product quality also involves delivery.
Therefore:
40/50 = 80%
Thus, Marcus maintains that 80% of the complaints involving billing also involve delivery.
Drop-down 2:
According to Elena’s diagram, the complaints already classified as involving delivery account for:
28% + 20% + 17% + 12% = 77%
Marcus also says that the 5% involving product quality only and the 8% involving billing and product quality also involve delivery.
Therefore:
77% + 5% + 8% = 90%
Thus, Marcus maintains that 90% of all complaints involve delivery.
Yes, you've got both right: 80 for the first blank and 90 for the second. Here's the reasoning so it clicks.
The key move is Marcus's one rule: every product-quality complaint must also involve delivery. So look at Elena's diagram and find the only two product-quality regions that don't touch the Delivery circle:
- Billing ∩ Product quality = 8% (the 8% lens between Billing and Product quality, outside Delivery) - Product quality only = 5% (the 5% at the bottom)
Marcus slides each of these into Delivery:
- The 8% joins the center - all-three region becomes 12 + 8 = 20% - The 5% joins Delivery ∩ Product quality - 17 + 5 = 22%
Everything else stays as Elena had it.
Blank 1 - billing that also involves delivery
All billing complaints: Billing only 10 + Billing ∩ Delivery 20 + all three 20 = 50%.
Billing and delivery: Billing ∩ Delivery 20 + all three 20 = 40%.
Therefore the fraction is 40 / 50 = 80%. Note the base here is billing complaints (50%), not all complaints - that's the spot that trips people up.
Blank 2 - all complaints involving delivery
Add every region inside the Delivery circle after Marcus's shift:
- Delivery only 28 - Billing ∩ Delivery 20 - All three 20 - Delivery ∩ Product quality 22
Total = 90%.
So 80% and 90% are correct. The whole question hinges on remembering to move both delivery-free product-quality regions (the 8% and the 5%) before you count.