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655-705 (Hard)|   Non-Math Related|   Tables|               
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General Discussion
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­This question should be in the table analysis category, not the graphs category
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chini
­This question should be in the table analysis category, not the graphs category
­Changed the tag. Thank you.
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Hi, can someone please explain how we got the answer to Q2.
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Thank you so much for your response!

Bismuth83
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Hi, can someone please explain how we got the answer to Q2.
Sure thing!

I believe that there might be some confusion as how to compare the chronology of "most" albums.

We can do this by considering the median. For Columbia, we have: 1928, 1959, 1959, 1959 \(\rightarrow\) 1959. For Blue Note: 1957, 1958, 1958, 1964, 1965 \(\rightarrow\) 1958.

3 Blue Note (most) albums were released before 1959 (1957, 1958, 1958), which means that most Blue Note albums weren't released later than most Columbia albums.
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Hi! I'm one of those confusing people :lol: Using the median seems like a logical way to get this one right, but I find it hard to get my mind around that idea. For example:
- If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer.
- If we compare the latest dates of Columbia albums with those of Blue Note Albums, we have the "NO" answer

Could you please point out the flaws in my thinking? Thank you

Bismuth83
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Hi, can someone please explain how we got the answer to Q2.
Sure thing!

I believe that there might be some confusion as how to compare the chronology of "most" albums.

We can do this by considering the median. For Columbia, we have: 1928, 1959, 1959, 1959 \(\rightarrow\) 1959. For Blue Note: 1957, 1958, 1958, 1964, 1965 \(\rightarrow\) 1958.

3 Blue Note (most) albums were released before 1959 (1957, 1958, 1958), which means that most Blue Note albums weren't released later than most Columbia albums.
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nvuluan
Hi! I'm one of those confusing people :lol: Using the median seems like a logical way to get this one right, but I find it hard to get my mind around that idea. For example:
- If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer.
- If we compare the latest dates of Columbia albums with those of Blue Note Albums, we have the "NO" answer

Could you please point out the flaws in my thinking? Thank you

Bismuth83
Nonbiryani
Hi, can someone please explain how we got the answer to Q2.
Sure thing!

I believe that there might be some confusion as how to compare the chronology of "most" albums.

We can do this by considering the median. For Columbia, we have: 1928, 1959, 1959, 1959 \(\rightarrow\) 1959. For Blue Note: 1957, 1958, 1958, 1964, 1965 \(\rightarrow\) 1958.

3 Blue Note (most) albums were released before 1959 (1957, 1958, 1958), which means that most Blue Note albums weren't released later than most Columbia albums.
I agree with you that using the median is weird. I'm a little bit stuck on "If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer." This part we wouldn't get any answer since you can't compare the two sets (1958 < 1959 but 1964 & 1965 are larger).

Think of this as 2 cases. We can consider each case and try to see if it'll work.
Case#1 is most Blue Note albums were released later than most Columbia albums. Here, we want to pick the newest majority of Blue Note albums and the oldest majority of Columbia albums. This would be sets (1958, 1964, 1965) and (1928,1959). However, they merge and thus the case won't work.

Case#2 is most Blue Note albums weren't released later than most Columbia albums. Here, we want to pick the oldest majority of Blue Note albums and the newest majority of Columbia albums. This would be sets (1957, 1958, 1958) and (1959,1959). These two sets don't merge and clearly match the inequality. So, this case works.
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Your case #1's description perfectly captures my predicament in the quotation. Only when I listed out the data just as you showed in case#2, I instantly recognized the right answer. It is strange but I guess its a good lesson to learn writing data out in order. Incidentally, do you think it's because the concept of time (release later), we must take the comparison with the most latest date (in order) of the released Columbia albums.
For example, considering this alternative data set:
- Columbia Albums (1959, 1958, 1958, 1928) vs Blue Note Albums (1964, 1965, 1958, 1958, 1957)
Would the answer still be "NO" in this case?

p/s: it has been a very productive discussion with you. appreciate very much for your time
Bismuth83
nvuluan
Hi! I'm one of those confusing people :lol: Using the median seems like a logical way to get this one right, but I find it hard to get my mind around that idea. For example:
- If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer.
- If we compare the latest dates of Columbia albums with those of Blue Note Albums, we have the "NO" answer

Could you please point out the flaws in my thinking? Thank you

Bismuth83
I agree with you that using the median is weird. I'm a little bit stuck on "If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer." This part we wouldn't get any answer since you can't compare the two sets (1958 < 1959 but 1964 & 1965 are larger).

Think of this as 2 cases. We can consider each case and try to see if it'll work.
Case#1 is most Blue Note albums were released later than most Columbia albums. Here, we want to pick the newest majority of Blue Note albums and the oldest majority of Columbia albums. This would be sets (1958, 1964, 1965) and (1928,1959). However, they merge and thus the case won't work.

Case#2 is most Blue Note albums weren't released later than most Columbia albums. Here, we want to pick the oldest majority of Blue Note albums and the newest majority of Columbia albums. This would be sets (1957, 1958, 1958) and (1959,1959). These two sets don't merge and clearly match the inequality. So, this case works.
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Most of the Blue Note albums listed were released later than most of the Columbia albums listed.
Solution:
To answer this, please understand that we need to compare the timeline of both the albums listed.
Release year Album
1928 Columbia
1957 Blue Note
1958 Blue Note
1958 Blue Note
1959 Columbia
1959 Columbia
1959 Columbia
1964 Blue Note
1965 Blue Note

We can see that 3 Blue note albums were released prior to Columbia.
Hence, No.

Let me know if you didn't follow.
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nvuluan
Your case #1's description perfectly captures my predicament in the quotation. Only when I listed out the data just as you showed in case#2, I instantly recognized the right answer. It is strange but I guess its a good lesson to learn writing data out in order. Incidentally, do you think it's because the concept of time (release later), we must take the comparison with the most latest date (in order) of the released Columbia albums.
For example, considering this alternative data set:
- Columbia Albums (1959, 1958, 1958, 1928) vs Blue Note Albums (1964, 1965, 1958, 1958, 1957)
Would the answer still be "NO" in this case?

p/s: it has been a very productive discussion with you. appreciate very much for your time
Bismuth83
nvuluan
Hi! I'm one of those confusing people :lol: Using the median seems like a logical way to get this one right, but I find it hard to get my mind around that idea. For example:
- If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer.
- If we compare the latest dates of Columbia albums with those of Blue Note Albums, we have the "NO" answer

Could you please point out the flaws in my thinking? Thank you

Bismuth83
I agree with you that using the median is weird. I'm a little bit stuck on "If we compare the bottom half of Columbia albums (1928, 1959 - still most) with the top three of Blue Note albums (1958, 1964 & 1965), we have the "YES" answer." This part we wouldn't get any answer since you can't compare the two sets (1958 < 1959 but 1964 & 1965 are larger).

Think of this as 2 cases. We can consider each case and try to see if it'll work.
Case#1 is most Blue Note albums were released later than most Columbia albums. Here, we want to pick the newest majority of Blue Note albums and the oldest majority of Columbia albums. This would be sets (1958, 1964, 1965) and (1928,1959). However, they merge and thus the case won't work.

Case#2 is most Blue Note albums weren't released later than most Columbia albums. Here, we want to pick the oldest majority of Blue Note albums and the newest majority of Columbia albums. This would be sets (1957, 1958, 1958) and (1959,1959). These two sets don't merge and clearly match the inequality. So, this case works.
I see where you are going. When the question asks to compare the majority of 2 sets, there is no criteria given to pick the majority. So, we'd have to assume that if it works for a chosen 2 majorities then it fulfills the inequality.

In your example, I'd say that there isn't enough information to decide. Since you have 2 different band albums in the same year, you can't compare them and thus you can't compare the majorities.
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Given: A table listing a jazz critic’s rankings of 16 jazz albums, including each album’s main artist, title, label, style, and year of release.

To find: For each statement, determine whether it is true based on the table.

Solution:

Statement 1: The most recent hard bop album listed is a John Coltrane album.
  • First, sort by “Style” and identify hard bop albums. There are 4 hard bop albums.
  • Compare their release years to find the latest year. The latest year among them is 1959.
  • Check the artist of the 1959 hard bop album. It is John Coltrane (Giant Steps).

Mark 'Yes'

Statement 2: Most of the Blue Note albums listed were released later than most of the Columbia albums listed.
  • Sort by Label. Identify all albums by ‘Blue Note’ and ‘Columbia’: Blue Note albums = 5, Columbia albums = 4
  • Note the year of release, one label at a time- Blue Note: three albums from 1957–1958, two from 1964–1965 and Columbia: three albums from 1959, one from 1928
  • If we consider the 3 Blue Note albums from 1957-58, they were released later than just one Columbia album. That is not MOST of Columbia albums.
  • Similarly, if we consider the two Blue Note albums from 1964-65, were released later than all Columbia albums. But this time it is not MOST of Blue Note albums.

Mark 'No'

Statement 3: At least half of the albums listed as being released in the 1950s were in the hard bop style.
  • Sort by Year and count albums from 1950–1959. There is a total of 9 albums.
  • Count hard bop albums within those 9. Total = 4.
  • Half of 9 would be at least 4.5 --- requires at least 5. Since only 4 are hard bop, the statement is false.

Mark 'No'


Correct Answer: Yes, No, No

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Hi jnxci,

Great question! You're really digging into the logic here, which is exactly the right approach.

The phrase 'Most of the Blue Note albums were released later than most of the Columbia albums' requires a two-step check:

Step 1: Determine what 'most of the Columbia albums' means as a benchmark. 'Most' means more than half. So a Blue Note album qualifies as 'released later than most Columbia albums' if it was released later than more than half of the individual Columbia albums.

Step 2: Check whether more than half of the Blue Note albums pass that test.

Now let's apply this to your alternative dataset:

Columbia albums: 1928, 1958, 1958, 1959 (4 albums). To be 'later than most,' a Blue Note album must be later than at least 3 of these 4 — meaning it must be released after 1958, so 1959 or later.

Blue Note albums: 1957, 1958, 1958, 1964, 1965 (5 albums). Which ones are later than 1958?
- 1957 → No (later than only 1 of 4)
- 1958 → No (later than only 1 of 4, since 1958 is not later than 1958)
- 1958 → No (same reason)
- 1964 → Yes (later than all 4)
- 1965 → Yes (later than all 4)

So only 2 out of 5 Blue Note albums pass the test. Since 2 is NOT most of 5 (you'd need at least 3), the answer would still be NO.

Key Takeaway: You don't compare to the latest Columbia date — you compare each Blue Note album against the whole set of Columbia albums individually, checking if it beats more than half of them. Then you see if more than half of the Blue Note albums achieved that. It's a nested 'more than half' check.

Common mistake: comparing only against the single highest or median Columbia date, rather than checking each Blue Note album against all individual Columbia albums.

Answer: Yes, No, No
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Question 2:
If you notice only 1964 one and 1965 of BlueStone clearly outshine that of Columbia, the remaining are stuck before 1959 and since Columbia has 3 years listed as 1959 you need to have values above 1959 to exceed the "most" category.
We only have two for BlueStone which is again not "most" it is 2/5
Thus answer is NO.
guddo
­The table shows a jazz critic’s rankings of the sixteen best jazz albums.

RankMain artistTitleLabelStyleYear
1Miles DavisKind of BlueColumbiamodal1959
2John ColtraneA Love SupremeImpulse!avant-garde1964
3Charles MingusMingus Ah UmColumbiasoul jazz1959
4Dave BrubeckTime OutColumbiaWest Coast1959
5Cannonball AdderlySomethin' ElseBlue Notehard bop1958
6Sonny RollinsSaxophone ColossusPrestigemixed1956
7John ColtraneGiant StepsAtlantichard bop1959
8Art BlakelyMoanin'Blue Notehard bop1958
9Herbie HancockMaiden VoyageBlue Notemodal1965
10Thelonious MonkBrilliant CornersRiversidebebop1956
11Bill EvansWaltz for DebbyRiversidemodal1961
12Keith JarrettThe Köln ConcertUniversalfree jazz1975
13Stan Getz, João GilbertoGetz/GilbertoVervebossa nova1963
14Eric DolphyOut to Lunch!Blue Noteavant-garde1964
15John ColtraneBlue TrainBlue Notehard bop1957
16Louis ArmstrongHot Fives & SevensColumbiaDixieland1928

For each of the following statements, select Yes if the statement is true based on the information provided. Otherwise select No.

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