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Employees at a certain company were asked to choose which of four meth 19 May 2024, 00:56
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Dropdown 1: more than 50 percent Dropdown 2: Print
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:

59% (02:05) correct 41% (02:16) wrong based on 2122 sessions

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­

Employees at a certain company were asked to choose which of four methods of training-visual, aural, print, and kinesthetic-to include in an upcoming training seminar. Each respondent to the survey chose from one to four of the methods. For each of the four methods, the chart shows the percentage of respondents who chose only that method. The chart also shows the percentage of respondents who chose exactly two of the methods, exactly three of the methods, and all four of the methods.

Select from the drop-down menus the options that create the statement that is most strongly supported by the information provided.

It must be the case that of the employees chose the method.­
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Dropdown 1: more than 50 percent Dropdown 2: Print
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Employees at a certain company were asked to choose which of four meth 19 May 2024, 10:25
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jack5397
­

Employees at a certain company were asked to choose which of four methods of training-visual, aural, print, and kinesthetic-to include in an upcoming training seminar. Each respondent to the survey chose from one to four of the methods. For each of the four methods, the chart shows the percentage of respondents who chose only that method. The chart also shows the percentage of respondents who chose exactly two of the methods, exactly three of the methods, and all four of the methods.

Select from the drop-down menus the options that create the statement that is most strongly supported by the information provided.

It must be the case that of the employees chose the method.­
Show more
­Yes jack5397, it is a question with four overlapping set.

Dropdown 2 gives all the four cases, so we have to focus on the Dropdown 1.

The various options are 
<25%: As all four overlap is 31.9%, so surely all of them are above that...Discard
25-50% and 50% are the other possible cases. But can we say that any of visual, aural, print, and kinesthetic would surely fall in any of the two ranges. So, let us check.

visual: 31.9% + 3.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 35% + x, where x could be 0 to 27%. Range = 35% to 35+27 or 62%. Hence, could fall in any of the two ranges 25-50 or >50.

aural: 31.9% + 7.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 39% + x, where x could be 0 to 27%. Range = 39% to 39+27 or 66%. Hence, could fall in any of the two ranges 25-50 or >50.

print: 31.9% + 19.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 51% + x, where x could be 0 to 27%. Range = 51% to 51+27 or 78%. Hence, would surely fall in the range >50...Answer

kinesthetic: 31.9% + 11.8% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 43.7% + x, where x could be 0 to 27%. Range = 43.7% to 43.7+27 or 70.7%. Hence, could fall in any of the two ranges 25-50 or >50.

Solution: Greater than 50% and Print
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Employees at a certain company were asked to choose which of four meth 19 May 2024, 01:27
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@chetan2u

Can you pls tell how to solve this question as it looks like 4 overlapping sets
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Employees at a certain company were asked to choose which of four meth 19 May 2024, 02:12
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Hi! As we know only one and all four, we can conclude that Printing has more than 50 percent. It might have some part of only two and only three as well but more than 50 we are already sure of.

Posted from my mobile device
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Employees at a certain company were asked to choose which of four meth 19 May 2024, 03:27
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Hi! As we know only one and all four, we can conclude that Printing has more than 50 percent. It might have some part of only two and only three as well but more than 50 we are already sure of.

Posted from my mobile device
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­I can't understand this if we know only one and all four then we can conclude that printing has more than 50%.

Can you pls elaborate and show the calculation amounting to more than 50%.
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Employees at a certain company were asked to choose which of four meth 20 May 2024, 05:06
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chetan2u

jack5397
­

Employees at a certain company were asked to choose which of four methods of training-visual, aural, print, and kinesthetic-to include in an upcoming training seminar. Each respondent to the survey chose from one to four of the methods. For each of the four methods, the chart shows the percentage of respondents who chose only that method. The chart also shows the percentage of respondents who chose exactly two of the methods, exactly three of the methods, and all four of the methods.

Select from the drop-down menus the options that create the statement that is most strongly supported by the information provided.

It must be the case that of the employees chose the method.­
­Yes jack5397, it is a question with four overlapping set.

Dropdown 2 gives all the four cases, so we have to focus on the Dropdown 1.

The various options are 
<25%: As all four overlap is 31.9%, so surely all of them are above that...Discard
25-50% and 50% are the other possible cases. But can we say that any of visual, aural, print, and kinesthetic would surely fall in any of the two ranges. So, let us check.

visual: 31.9% + 3.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 35% + x, where x could be 0 to 27%. Range = 35% to 35+27 or 62%. Hence, could fall in any of the two ranges 25-50 or >50.

aural: 31.9% + 7.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 39% + x, where x could be 0 to 27%. Range = 39% to 39+27 or 66%. Hence, could fall in any of the two ranges 25-50 or >50.

print: 31.9% + 19.1% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 51% + x, where x could be 0 to 27%. Range = 51% to 51+27 or 78%. Hence, would surely fall in the range >50...Answer

kinesthetic: 31.9% + 11.8% + possibly some or most part of (14.9%(exactly two) +  12.1%(exactly three)). Thus 43.7% + x, where x could be 0 to 27%. Range = 43.7% to 43.7+27 or 70.7%. Hence, could fall in any of the two ranges 25-50 or >50.

Solution: Greater than 50% and Print
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­Thank you so much, this is very helpful.
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Employees at a certain company were asked to choose which of four meth 29 Oct 2024, 04:57
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chetan2u I'm unable to understand the calculations here:

visual: 31.9% + 3.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 35% + x, where x could be 0 to 27%. Range = 35% to 35+27 or 62%. Hence, could fall in any of the two ranges 25-50 or >50.

Can you please explain why did we start with adding adding 31.9% at the first?

Thank you
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Employees at a certain company were asked to choose which of four meth 02 Nov 2024, 16:04
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We can see that 19.1% of total employees chose the print method.(We are sure about this through the diagram.)
Moreover, we can see that 31.9% of total employees chose the print method. (Visible through the diagram.). This means that 31.9% of total employees said yes to all 4 method i.e, print/visual/aural and kinesthetic.
Hence, 51% of total employees said yes to Print method. This must be the case. Hence, the correct answer is more than 50% in first blank and print in the second.

P.S: This is must be true question. We are sure about the above mentioned data points with utmost certainty.
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Employees at a certain company were asked to choose which of four meth 07 Nov 2024, 00:09
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the answer is :

31.9% (Total employess) ---> All 4
19.1% (Total employess) ---> print
therefore ---> 31.9+19.1 = 51%(Total employess) must be in the print
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Employees at a certain company were asked to choose which of four meth 10 Nov 2024, 03:33
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4 set venn diagram incase anyone wants to visualize
Although the numbers are such that observation is enough to answer the question
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Although the numbers are such that observation is enough to answer the question
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Employees at a certain company were asked to choose which of four meth 30 Jul 2025, 12:16
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chetan2u
Why did you add all four to the other choices? If all 4 were selected that automatically includes the other choices, The question does not specifically say that the respondents chose only one of the choices.
chetan2u
jack5397
­

Employees at a certain company were asked to choose which of four methods of training-visual, aural, print, and kinesthetic-to include in an upcoming training seminar. Each respondent to the survey chose from one to four of the methods. For each of the four methods, the chart shows the percentage of respondents who chose only that method. The chart also shows the percentage of respondents who chose exactly two of the methods, exactly three of the methods, and all four of the methods.

Select from the drop-down menus the options that create the statement that is most strongly supported by the information provided.

It must be the case that of the employees chose the method.­
­Yes jack5397, it is a question with four overlapping set.

Dropdown 2 gives all the four cases, so we have to focus on the Dropdown 1.

The various options are
<25%: As all four overlap is 31.9%, so surely all of them are above that...Discard
25-50% and 50% are the other possible cases. But can we say that any of visual, aural, print, and kinesthetic would surely fall in any of the two ranges. So, let us check.

visual: 31.9% + 3.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 35% + x, where x could be 0 to 27%. Range = 35% to 35+27 or 62%. Hence, could fall in any of the two ranges 25-50 or >50.

aural: 31.9% + 7.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 39% + x, where x could be 0 to 27%. Range = 39% to 39+27 or 66%. Hence, could fall in any of the two ranges 25-50 or >50.

print: 31.9% + 19.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 51% + x, where x could be 0 to 27%. Range = 51% to 51+27 or 78%. Hence, would surely fall in the range >50...Answer

kinesthetic: 31.9% + 11.8% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 43.7% + x, where x could be 0 to 27%. Range = 43.7% to 43.7+27 or 70.7%. Hence, could fall in any of the two ranges 25-50 or >50.

Solution: Greater than 50% and Print
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Employees at a certain company were asked to choose which of four meth 05 Aug 2025, 16:36
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Because by selecting all 4 they inherently select each one. You can therefore add 31.9% to each.
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chetan2u
Why did you add all four to the other choices? If all 4 were selected that automatically includes the other choices, The question does not specifically say that the respondents chose only one of the choices.
chetan2u
jack5397
­

Employees at a certain company were asked to choose which of four methods of training-visual, aural, print, and kinesthetic-to include in an upcoming training seminar. Each respondent to the survey chose from one to four of the methods. For each of the four methods, the chart shows the percentage of respondents who chose only that method. The chart also shows the percentage of respondents who chose exactly two of the methods, exactly three of the methods, and all four of the methods.

Select from the drop-down menus the options that create the statement that is most strongly supported by the information provided.

It must be the case that of the employees chose the method.­
­Yes jack5397, it is a question with four overlapping set.

Dropdown 2 gives all the four cases, so we have to focus on the Dropdown 1.

The various options are
<25%: As all four overlap is 31.9%, so surely all of them are above that...Discard
25-50% and 50% are the other possible cases. But can we say that any of visual, aural, print, and kinesthetic would surely fall in any of the two ranges. So, let us check.

visual: 31.9% + 3.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 35% + x, where x could be 0 to 27%. Range = 35% to 35+27 or 62%. Hence, could fall in any of the two ranges 25-50 or >50.

aural: 31.9% + 7.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 39% + x, where x could be 0 to 27%. Range = 39% to 39+27 or 66%. Hence, could fall in any of the two ranges 25-50 or >50.

print: 31.9% + 19.1% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 51% + x, where x could be 0 to 27%. Range = 51% to 51+27 or 78%. Hence, would surely fall in the range >50...Answer

kinesthetic: 31.9% + 11.8% + possibly some or most part of (14.9%(exactly two) + 12.1%(exactly three)). Thus 43.7% + x, where x could be 0 to 27%. Range = 43.7% to 43.7+27 or 70.7%. Hence, could fall in any of the two ranges 25-50 or >50.

Solution: Greater than 50% and Print
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Employees at a certain company were asked to choose which of four meth 21 Aug 2025, 22:49
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I was initially confused by the solutions explained earlier, wondering why aren't we considering exactly two or exactly three. For those who are still confused even after going through earlier discussions, here is an explanation:
In the tutorials posted by experts earlier, for questions that involve 'must', we have to take the worst-case scenarios => Minimum number possible. It is possible that in exactly two or exactly three scenarios, Print might still not be considered. Eg: Exactly Two - (Visual + Aural), (Kinestetic + Aural), etc. Exactly three - (Visual + Aural + Kinestetic) . Since these scenarios can also come up apart from the ones explained in the very first solution, we have to consider worst case where Print is surely included. Those cases are: (Print only) + (Exactly four). It is a bare minimum condition that should hold true (required to get the answer).

Print = 19.1% + 31.9%
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Employees at a certain company were asked to choose which of four meth 11 Nov 2025, 03:11
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What the chart shows
  • Four training methods: visual, aural, print, kinesthetic
  • Slices for "only visual/aural/print/kinesthetic” and for “exactly two,” “exactly three,” and “all four”
  • Key slice values: visual only 3.1%, aural only 7.1%, kinesthetic only 11.8%, print only 19.1%, exactly two 14.9%, exactly three 12.1%, all four 31.9%
  • Must‐be‐true logic
  • For any method, at least the people who chose “only that method” plus the people who chose “all four” definitely chose it


  • Minimum guaranteed for each method:
      Visual: 3.1% + 31.9% = 35.0%Aural: 7.1% + 31.9% = 39.0%Kinesthetic: 11.8% + 31.9% = 43.7%Print: 19.1% + 31.9% = 51.0%

  • Only print is guaranteed to be above 50%.

  • So the correct fill-ins are “more than 50 percent” and “print"
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Employees at a certain company were asked to choose which of four meth 11 Nov 2025, 03:20
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Why did you add all four to the other choices? If all 4 were selected that automatically includes the other choices, The question does not specifically say that the respondents chose only one of the choices.
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All four must be added because everyone in that slice chose every method, so they definitely count toward each method’s total. The chart explicitly separates “only X” from “exactly two,” “exactly three,” and “all four,” so totals for a method include several slices, not just the “only” slice
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