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19 May 2025, 11:19
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If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category.: True
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category.: True
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown.: False
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
60% (03:23) correct
40%
(03:21)
wrong
based on 150
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The table summarizes 2021 data for ten product categories sold by Company Y, a national retailer in Country X. For each category, the table shows:
• The percentage of total national sales (measured in dollars) accounted for by Company Y, and its rank based on that percentage
• The percentage of total national units sold accounted for by Company Y, and its rank based on that percentage
For each of the following statements, select True if the statement can be verified as true based on the information provided. Otherwise, select False.
• The percentage of total national sales (measured in dollars) accounted for by Company Y, and its rank based on that percentage
• The percentage of total national units sold accounted for by Company Y, and its rank based on that percentage
| Product Category | Company’s Share of Total National Sales | Rank by Sales Share | Company’s Share of Total National Units Sold | Rank by Units Sold |
|---|---|---|---|---|
| Apparel | 26% | 2 | 24% | 4 |
| Cleaning Supplies | 7% | 9 | 12% | 8 |
| Electronics | 49.5% | 2 | 32% | 2 |
| Footwear | 41% | 2 | 43% | 1 |
| Furniture | 74.5% | 1 | 35% | 2 |
| Home Decor | 33% | 2 | 22% | 4 |
| Packaged Food | 36.6% | 2 | 16% | 5 |
| Personal Care | 14% | 5 | 18% | 4 |
| Pet Supplies | 9.5% | 7 | 10% | 9 |
| Stationery | 4.5% | 10 | 7% | 10 |
For each of the following statements, select True if the statement can be verified as true based on the information provided. Otherwise, select False.
| True | False | |
| If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category. | ||
| If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category. | ||
| Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown. |
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Official Answer
If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category.: True
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category.: True
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown.: False
28 May 2025, 03:15
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Official Solution:
If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category.
• Company Y had 49.5% of total national sales in Electronics and was ranked 2nd, meaning one other company had more than 49.5%. That leaves less than 1% of the market for any other companies combined. Since the condition states that no company had less than or equal to 1%, no third company could exist in this category. Therefore, only two companies could have accounted for national sales in Electronics.
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category.
• Company Y had 24% of national units sold in Apparel and was ranked 4th, meaning at least three other companies had more than or equal to 24%. Thus, these four companies accounted for more than 4 * 24% = 96%. So, less than 4% remains for any additional companies. Since no company had less than or equal to 2%, only one more company can fit into the remaining share. Therefore, at most five companies could have accounted for units sold in Apparel.
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown.
• To compare medians, we list all ten ranks by sales share and units sold in order. Company Y’s ranks by sales share are: 1, 2, 2, 2, 2, 2, 5, 7, 9, 10. The median is the average of the 5th and 6th values: (2 + 2)/2 = 2. For units sold, the ranks are: 1, 2, 3, 4, 4, 4, 5, 8, 9, 10. The median is the average of the 5th and 6th values: (4 + 4)/2 = 4. Since the medians are not equal, the statement is false.
Correct answer:
If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category. "True"
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category. "True"
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown. "False"
Bunuel
If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category.
• Company Y had 49.5% of total national sales in Electronics and was ranked 2nd, meaning one other company had more than 49.5%. That leaves less than 1% of the market for any other companies combined. Since the condition states that no company had less than or equal to 1%, no third company could exist in this category. Therefore, only two companies could have accounted for national sales in Electronics.
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category.
• Company Y had 24% of national units sold in Apparel and was ranked 4th, meaning at least three other companies had more than or equal to 24%. Thus, these four companies accounted for more than 4 * 24% = 96%. So, less than 4% remains for any additional companies. Since no company had less than or equal to 2%, only one more company can fit into the remaining share. Therefore, at most five companies could have accounted for units sold in Apparel.
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown.
• To compare medians, we list all ten ranks by sales share and units sold in order. Company Y’s ranks by sales share are: 1, 2, 2, 2, 2, 2, 5, 7, 9, 10. The median is the average of the 5th and 6th values: (2 + 2)/2 = 2. For units sold, the ranks are: 1, 2, 3, 4, 4, 4, 5, 8, 9, 10. The median is the average of the 5th and 6th values: (4 + 4)/2 = 4. Since the medians are not equal, the statement is false.
Correct answer:
If no company had less than or equal to 1% of total national sales in Electronics, then only two companies accounted for national sales in that category. "True"
If no company had less than or equal to 2% of total national units sold in Apparel, then at most five companies accounted for units sold in that category. "True"
Company Y’s median rank by sales share is equal to its median rank by units sold across all product categories shown. "False"
28 May 2025, 08:43
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For the Second Question, you said, "meaning at least three other companies had more than or equal to 24%":
Case1: More Than: Evaluating more than: 24%, 25%, 26%, 27% (Ranks 4, 3, 2, 1 respectively, by units sold, let's say) ... wont be possible because: 24+25+26+27= 102, so not possible, even in the case of 24+25+25+25= 99 not possible (as % share for the 5th company can't be less than or equal to "2")
Case2: Equal to: if all the top 4 companies have 24% of units sold in the market, then why is the rank of the 'y' company rank 4?, it is the highest as any of its competitors, it should too have rank #1 in the number of units sold, isn't it?
Therefore, I think the answer should be "No", the info. can't be verified! Bunuel, please share your view.
Making Answers as: True, False, False
Case1: More Than: Evaluating more than: 24%, 25%, 26%, 27% (Ranks 4, 3, 2, 1 respectively, by units sold, let's say) ... wont be possible because: 24+25+26+27= 102, so not possible, even in the case of 24+25+25+25= 99 not possible (as % share for the 5th company can't be less than or equal to "2")
Case2: Equal to: if all the top 4 companies have 24% of units sold in the market, then why is the rank of the 'y' company rank 4?, it is the highest as any of its competitors, it should too have rank #1 in the number of units sold, isn't it?
Therefore, I think the answer should be "No", the info. can't be verified! Bunuel, please share your view.
Making Answers as: True, False, False
Bunuel
