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805+ (Hard)|   Math Related|   Tables|            
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Why is statement 3 wrong? "Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category."

Hence, he will donate to any category which has more than 1 star. Civica has 3 and 4 stars in Finance and Accountability respectively.
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Why is statement 3 wrong? "Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category."

Hence, he will donate to any category which has more than 1 star. Civica has 3 and 4 stars in Finance and Accountability respectively.
In the Community category, for finances, Civica has 3 stars while Together We Will has 4 stars. So, Civica is not as highly rated in finances as Together We Will, which is in the same category as Civica.

So, since Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category, we see that Gordon will not donate to Civica.
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In the Community category, for finances, Civica has 3 stars while Together We Will has 4 stars. So, Civica is not as highly rated in finances as Together We Will, which is in the same category as Civica.

So, since Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category, we see that Gordon will not donate to Civica.


By as highly rated as any of the other charities what does the question mean? Should both categories be the highest rated or should not be the lowest rated? MartyMurray
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By as highly rated as any of the other charities what does the question mean? Should both categories be the highest rated or should not be the lowest rated? MartyMurray
Here's the complete statement from the passage:

Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category.

"At least as highly rated as" means "not rated lower than."

So, for Gordon to donate, a charity cannot be rated lower for finances or accountability than any other in the same category. It can be rated only the same as or higher than others in the same category.
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Statement 1

Gordon will donate to at least one of these charities.

To see whether the information provided indicates whether Gordon will donate to at least one of these charities, we can go back to the passage to review what it says. Doing so, we find the following:

    seven charities to which Gordon is considering donating money

    Gordon may have other criteria that would prevent him from donating to one or more of these charities.

We see that the text indicates that Gordon is "considering" donating. So, he has not decided to donate money. Also, other criteria may "prevent" him from donating.

Thus, it may be that he will not donate to any of the charities. So, statement 1 is not supported.



That's very tricky.

I met some questions in DI similar to this one and got wrong each time, because I always considered such intentionally vague claims—contradicting to other more detailed information in the passage—no more than a distraction, though I indeed noticed them.
I learned a lot.

Thank you Marty.
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No Community charity qualifies
Environment charity (Green World) qualifies
Health charity (Healthy Hearts) qualifies


1. G­ordon will donate to at least one of these charities. => Does not statement is correct

Because Gordon may have other criteria that would prevent him from donating to one or more of these charities

2. Gordon will donate to at most one of these charities. => Does not indicate statement is correct

At most 2

3. Gordon will not donate to a charity in the Community category. => Indicate statement is correct

As worked out above
 ­
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The table shows a website's ratings of the finances and accountability of each of seven charities to which Gordon is considering donating money. Greater numbers of asterisks (*) indicate higher ratings. Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category. Gordon may have other criteria that would prevent him from donating to one or more of these charities.

NameCategoryFinancesAccountability
CivicaCommunity*******
Eco SocietyEnvironment****
Green WorldEnvironment*****
Healthy HeartsHealth*****
Nature's FriendsEnvironment****
Solutions in MedicineHealth****
Together We WillCommunity*****

For each of the following statements, select Indicates statement is correct if the information provided indicates that the statement is correct. Otherwise, select Does not indicate statement is correct.

ID: 700248
­

Sort by category and leave it at that.
Given: "Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category."
This means for Gordon to donate, a charity must have the highest * in both criteria given in that category. Another charity could have the same number of * but not more.

Gordon will donate to at least one of these charities.

Given: Gordon is considering donating money... Gordon may have other criteria that would prevent him from donating to one or more of these charities.

Even if a charity meets his requirements, he may still not donate. So we cannot say that he will donate to at least one of these. No other evaluation is required.

Select 'Does not indicate statement is correct'

Gordon will donate to at most one of these charities.

Here evaluation is required. What if only one charity satisfies his criteria? Then we know that he donate to at most 1. But if 2 or more charities satisfy his criteria then we cannot conclude this.
First 2 charities are community. Neither works since neither has more or equal number of *.
Next 3 are environment - Green World works - Highest number of * in both.
Next 2 are Health - Healthy Hearts works - Highest number of * in both.

There are two possible charities he could donate to. He may donate to both.

Select 'Does not indicate statement is correct'


Gordon will not donate to a charity in the Community category.

This is true. We saw above that in community category, neither charity works.

Select Indicates statement is correct

Here is a discussion on another official TA question: https://youtu.be/OyN_szEDEPw
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KarishmaB


Sort by category and leave it at that.
Given: "Gordon will NOT donate to a charity UNLESS, for both finances and accountability, it is at least as highly rated as any of the other charities in the same category."
This means for Gordon to donate, a charity must have the highest * in both criteria given in that category. Another charity could have the same number of * but not more.

Gordon will donate to at least one of these charities.

Given: Gordon is considering donating money... Gordon may have other criteria that would prevent him from donating to one or more of these charities.

Even if a charity meets his requirements, he may still not donate. So we cannot say that he will donate to at least one of these. No other evaluation is required.

Select 'Does not indicate statement is correct'

Gordon will donate to at most one of these charities.

Here evaluation is required. What if only one charity satisfies his criteria? Then we know that he donate to at most 1. But if 2 or more charities satisfy his criteria then we cannot conclude this.
First 2 charities are community. Neither works since neither has more or equal number of *.
Next 3 are environment - Green World works - Highest number of * in both.
Next 2 are Health - Healthy Hearts works - Highest number of * in both.

There are two possible charities he could donate to. He may donate to both.

Select 'Does not indicate statement is correct'


Gordon will not donate to a charity in the Community category.

This is true. We saw above that in community category, neither charity works.

Select Indicates statement is correct

Here is a discussion on another official TA question: https://youtu.be/OyN_szEDEPw

MartyMurray KarishmaB chetan2u Bunuel

Why do we require evaluation for the second statement ?
Statement says - "Gordon will donate to at most one of these charities."

Let's say in the table provided we only had 1 charity which satisfies the necessary condition mentioned. But still, there may be other factors - due to which Gordon may not donate to that charity.
The statement says "will donate" - "will" expresses certainty. So, irrespective of the number of charities, meeting the necessary condition - we can never be certainly sure whether Gordon will donate to the charity.

Am I comprehending the 2nd option in a wrong way ?
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MartyMurray KarishmaB chetan2u Bunuel

Why do we require evaluation for the second statement ?
Statement says - "Gordon will donate to at most one of these charities."

Let's say in the table provided we only had 1 charity which satisfies the necessary condition mentioned. But still, there may be other factors - due to which Gordon may not donate to that charity.
The statement says "will donate" - "will" expresses certainty. So, irrespective of the number of charities, meeting the necessary condition - we can never be certainly sure whether Gordon will donate to the charity.

Am I comprehending the 2nd option in a wrong way ?

Imagine a case where only one charity satisfies the criteria. In that case, saying that Gordon will donate to at most one of the charities would be correct, since “at most one” allows for zero or one.

However, if two charities satisfy the criteria, then saying that Gordon will donate to at most one would not be correct, because he could theoretically donate to two, so stating with certainty that he will donate to at most one would be incorrect.

Hope it's clear.
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Bunuel


Imagine a case where only one charity satisfies the criteria. In that case, saying that Gordon will donate to at most one of the charities would be correct, since “at most one” allows for zero or one.

However, if two charities satisfy the criteria, then saying that Gordon will donate to at most one would not be correct, because he could theoretically donate to two, so stating with certainty that he will donate to at most one would be incorrect.

Hope it's clear.
Oh okay! Got it...Thank you !

Bunuel - A follow up query - when you say "at most one allows for zero or one." - does this include both the cases? i.e. If from the table, we find that -
1. Gordon can donate to at least 1 charity - we mark "Indicates statement is correct"
2. Gordon can't donate to any charity - still do we mark "Indicates statement is correct" ???
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rushimehta

Oh okay! Got it...Thank you !

Bunuel - A follow up query - when you say "at most one allows for zero or one." - does this include both the cases? i.e. If from the table, we find that -
1. Gordon can donate to at least 1 charity - we mark "Indicates statement is correct"
2. Gordon can't donate to any charity - still do we mark "Indicates statement is correct" ???

Yes, exactly. “At most one” means zero or one, and both cases make the statement true.

So:

  1. If one charity qualifies, the statement holds.
  2. If no charity qualifies, it still holds (since zero ≤ one).

Only if two or more qualify would the statement be false.
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Seems like the difficulty is entirely caused by the necessary vs sufficient trap. I feel like someone who is coming to such questions after increasing proficiency in CR wouldn't fall for this trap.
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egmat - Hi, I have a doubt regarding the video solution and wanted to confirm my understanding.
The video mentions that a charity should not be the least rated in its category. However, I interpreted the condition differently after discussing it with ChatGPT.
Consider this hypothetical example:


CharityFinanceAccountability
Nature's Friends★★★
Green World★★★★★★
Eco Society★★★★★

The condition in the question states that the charity must be "at least as highly rated as any of the other charities in the same category" for both finances and accountability.
In this example:
  • Nature's Friends would be rejected because it is not highest in Finance.
  • Green World qualifies.
  • It seems that Eco Society should also be rejected, because although it is tied for the highest in Finance, it is not at least as highly rated as Green World in Accountability (★★★ vs ★★★★).
However, based on the explanation in the video, it sounded like only Nature's Friends would be rejected.
Could you please confirm whether my interpretation is correct, or if I'm missing something?


egmat
­Another brilliant question. Here are certain attributes of this question:
  1. The dataset presents a criterion.
  2. The table presents data for potential candidates.
  3. There is some other unstated criteria as well.

Based on the above, we need to determine which statement can be concluded and which cannot be concluded.

So, to answer this question effectively, we need to carefully understand the criterion presented – “Gordon will NOT donate to a charity UNLESS for both finances and accountability, it is at least as highly rated as any of the other charities in the same category.” This is a fairly loaded criterion. Watch the video at 1’ mark to see its translation in simple words.


Next, as you watch the video, pay close attention to the treatment of statement 1 vs. statement 2. There is only one word difference – at least and at most and given the scenario, the treatment is completely different for these two statements.

And then observe how the analysis of statement 2 helps answer statement 3.

So, all in all, amazing question that can be solved effectively if one applies the “owning the dataset” mindset.
­
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Hi Usernamevisible,

Your interpretation is correct, and the example you built is a genuinely good one.

The condition is: for both Finances and Accountability, the charity must be at least as highly rated as any of the other charities in the same category. Read strictly, "any" here means every - in each of the two columns, the charity's rating must be greater than or equal to every other rating in its category. So a qualifying charity has to sit at the top of both columns; a tie at the top is fine, but nothing may be above it.

Your hypothetical

Environment maxima in your table: Finances 2, Accountability 4.

- Nature's Friends: Finances 1 < 2, so out.
- Green World: 2 = max, 4 = max, so it qualifies.
- Eco Society: Finances 2 = max, but Accountability 3 < 4, so out.

So yes - Eco Society is rejected. You have read the condition correctly.

About the shortcut in the video

The video first restates the condition strictly, then simplifies it to this: you clear a column as long as there is at least one other charity in your category that you equal or beat. On this table that simplification selects the correct charities. Your table is what separates them - your Eco Society equals Nature's Friends at 3 in Accountability, so the simplified rule passes it, while the actual condition, which requires it to be at least as high as every other and Green World sits at 4, rejects it.

The real table

Environment maxima are Finances 2, Accountability 3. Eco Society (2, 2) fails Accountability; Nature's Friends (1, 3) fails Finances; only Green World clears both. No Community charity qualifies, and Healthy Hearts is the only qualifier in Health.

Answers: Statement 1 - Does not indicate statement is correct; Statement 2 - Does not indicate statement is correct; Statement 3 - Indicates statement is correct.

Usernamevisible
egmat - Hi, I have a doubt regarding the video solution and wanted to confirm my understanding.
The video mentions that a charity should not be the least rated in its category. However, I interpreted the condition differently after discussing it with ChatGPT.
Consider this hypothetical example:


CharityFinanceAccountability
Nature's Friends★★★
Green World★★★★★★
Eco Society★★★★★

The condition in the question states that the charity must be "at least as highly rated as any of the other charities in the same category" for both finances and accountability.
In this example:
  • Nature's Friends would be rejected because it is not highest in Finance.
  • Green World qualifies.
  • It seems that Eco Society should also be rejected, because although it is tied for the highest in Finance, it is not at least as highly rated as Green World in Accountability (★★★ vs ★★★★).
However, based on the explanation in the video, it sounded like only Nature's Friends would be rejected.
Could you please confirm whether my interpretation is correct, or if I'm missing something?



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