For each of 5 airlines (Airlines 1 through 5), the table shows the per

Question

For each of 5 airlines (Airlines 1 through 5), the table shows the percent of flights offered by that airline last year that were delayed by certain ranges of time to the nearest minute and the total percent of flights offered by that airline last year that were delayed. The airlines are numbered from greatest total number of flights offered last year (Airline 1) to least total number of flights offered last year (Airline 5).

TOUR CITIES

Airline  
   1 to 15   
   16 to 30   
   31 to 45   
   46 to 60   
   More than 60   
   Total delays   
 
   4  
 6.3% 
 4.8% 
 5% 
 1.7% 
 2.5% 
 20.3% 
 
   3  
 7.5% 
 7.1% 
 4.5% 
 2.2% 
 1.7% 
 23% 
 
   1  
 8.5% 
 6.5% 
 5.8% 
 2.1% 
 1.6% 
 24.5% 
 
   5  
 8.8% 
 5.9% 
 7.1% 
 1.9% 
 1.2% 
 24.9% 
 
   2  
 9.2% 
 6.9% 
 4.9% 
 2.4% 
 2.8% 
 26.2%

chetan2u · Accepted Answer

For each of 5 airlines (Airlines 1 through 5), the table shows the percent of flights offered by that airline last year that were delayed by certain ranges of time to the nearest minute and the total percent of flights offered by that airline last year that were delayed. The airlines are numbered from greatest total number of flights offered last year (Airline 1) to least total number of flights offered last year (Airline 5).

For each of the following statements about Airlines 1 through 5, select Must be true if the statement must be true if the information provided is also true. Otherwise, select Need not be true.

Must be true	Need not be true.	Statement
	✅	Airline 2 had the greatest number of flights last year that were delayed by 1 to 15 minutes, to the nearest minute.

Airline 2 has the highest % of delays in all but is the second largest contributor to number of flights. So, airline 2 had greater flights in the given category for 3, 4 and 5.
However, we do not know whether 6.3% of number of flights of airline 1 is less than 9.2% of number of flights of airline 2.
If airline 1 had 200 flights while airline 2 had 100 flights => 6.3% of 200>9.2% of 100
If airline 1 had 200 flights while airline 2 had 150 flights => 6.3% of 200<9.2% of 150

Must be true	Need not be true.	Statement
✅		Airline 5 had the least number of flights last year that were delayed by more than 60 minutes, to the nearest minute.

Airline has the least % of flights in the given category, 1.2%, and also has the least number of overall flights.
So least % of least number has to be the smallest of all.

Must be true	Need not be true.	Statement
✅		Airline 3 did NOT have the least number of total delayed flights last year.

Airline 4 has a lesser % and lesser total flights compared to airline 3. So surely airline 3 has more number of delayed flights as Concorde to airline 4.

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Answer: Need not be true, Must be true, and Must be true

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Attachment:

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KarishmaB · Answer

Note here that we do not know their total number of flights but we know that airline 1 had the maximum number of total flights and airline 5 had the minimum (in that order 1 to 5).

Airline 2 had the greatest number of flights last year that were delayed by 1 to 15 minutes, to the nearest minute.

9.2% of all flights of Airline 2 were delayed by 1 to 15 minutes and that is the highest percentage but does it mean that it also represents the highest number of flights? No. What if Airline 2 had twice the number of total flights compared with airline 2 and so its 8.5% (number of flights that were delayed by 1 to 15 minutes) would be far more than those of airline 2.

ANSWER: Need not be true

Airline 5 had the least number of flights last year that were delayed by more than 60 minutes, to the nearest minute.

Airline 5 had only 1.2% flights delayed by more than 60 minutes, the lowest percentage among all airlines. We also know that airline 5 had the least total number of flights. This means 1.2% of the least total number of flights is bound to give us the least number of flights delayed by more than 60 minutes.

ANSWER: Must be true

Airline 3 did NOT have the least number of total delayed flights last year.

Airline 3 had 23% total flights delayed. Airline 4 has 20.3% of total flights delayed. The total number of flights of airline 4 were less than those of airline 3. So a lower percentage of a lower base will certainly lead to a lower number. So airline 4 certainly had fewer delayed flights last year compared with airline 3. Then we can say that definitely airline 3 did NOT have the least number of total delayed flights last year.

ANSWER: Must be true

Check this video on percentages: 
 https://youtu.be/HxnsYI1Rws8

vasudevpant · Answer

Sir, I am still getting confused that why Case of Airline 2 must not be true

mmdfl · Answer

pre-thinking
- n_k = total ABSOLUTE number of flights last year for the Airline "k" (delayed+not delayed)
- The airlines are numbered from greates total number of flights offered last year to least total number, so:
n_1 > n_2 > n_3 > n_4 > n_5 (inneq. I)
- Let "percentage_k_a_to_b" be the percentage of flights offered by airline "k" last year that were delayed by the range [a,b] minutes (entries of the table)

what is been tested in this question
- your capacity to differentiate relative and absolute size (percentages, innequations)

Statement 1 states that n_2*(9.2%) > n_k*percentage_k_1_to_15, which is not necessarely true, because although 9.2% is the greatest value that percentage_k_1_to_15 can have, maybe n_1 is so big that n_1*8.5% > n_2*9.2%. We cant say whether is true or not. => "Need not be true"

Statement 2 says that n_5*1.2% < n_k*percentage_k_1_to_15, k!=5. This is indeed true because 1.2% < percentage_k_1_to_15, for every k!=5, according with the table, AND we also have that n_5<n_k, for each k!=5, according with "inneq. I". We obtain the original statement by multiplying both innequations. => "Must be true"

Statement 3 says "Airline 3 did NOT have the least number of total delayed flights last year.". This is the same as saying that there must be at least one other Airline that have a smaller number of total delayed flights last year. Putting in a more mathy term, we want to evaluate as being true or not whether there is at least one k!=3, such that n_k*percentage_k_total < n_3*23%. We want something that must be true without any doubt, so lets find n_k < n_3 AND percentage_k_total < 23%, in a similar approach as done on statement 2:
- n_k < n_3: k = 4 or 5
- percentage_k_total < 23%: k = 4
So we can absolutelly say that Airline 3 did NOT have the least number of total delayed flights last year, because Airline 4 had less that Airline 3. (PS: note that we are not saying that Airline 4 had the least number, since we don't have enough information about how n_5 is smaller that n_4)

Jake7Wimmer · Answer

The question says had the greatest  number  of flights. We are only given percentages. The passage states that the airlines are in order from greatest number of fights (1) to least (5). What if Airline 1 had a 100,000 more flights than airline 2. Wouldn't matter now that airline 2 had a greater percentage. Thus, no conclusion can be made.

electronuke · Answer

Here's a dumbed down explanation of why 2 and 3 are musts.
2. We know Airline 5 has the least number of passengers. Airline 5 also has the lowest percentage of delays over 60 minutes at 1.2%. Since both are the lowest, there must be the least number of delays.
3. We know Airline 4 and 5 had fewer number of passengers than Airline 3. If either had a fewer total delay % than Airline 3, then no matter what it would have fewer total delays than Airline 3. Since Airline 4 had a 20.3% total delay %, no matter what the number, Airline 4 will have fewer total delay %.
Logic: 
WHAT WE ARE SOLVING FOR: Lower than Airline 3 passengers * Lower % total delays < Airline 3# passengers * 23%
Airline 4: Lower # passenger * 20.3%. Since Lower # passengers and 20.3% < 23%, the before statement is true in this case.
Airline 5: Lower # passengers * 24.9% We don't know.
Since Airline 4 is lower # passengers and lower % total delays, it MUST be lower than Airline 3.

Jon22 · Answer

Airline 3 did NOT have the least number of total delayed flights last year.
 
  Airline 1  has  20.3%  total delays,  Airline 2  has  26.2% ,  Airline 3  has  24.5% ,  Airline 4  has  24.9% , and  Airline 5  has  23.0% . 
 Comparing the total delays:
 
 Airline 1: 20.3% 
 Airline 2: 26.2% 
 Airline 3: 24.5% 
 Airline 4: 24.9% 
 Airline 5: 23.0%  
  
Airline 1 has the least percentage of total delays, which means Airline 3 did  not  have the least total delayed flights.
 Conclusion :  Must be true.

HarshavardhanR · Answer

The airlines are numbered from greatest total number of flights offered last year (Airline 1) to least total number of flights offered last year (Airline 5).

The above line is super critical.

While we do not know the exact numbers of flights, we actually know which airline is higher/lower than which airline in terms of number of flights.

(1) Note that Airline 1 had more absolute number of flights than Airline 2.
 
 Even if Airline 2 has a higher % of 1-15 delayed flights (9.2>8.5), what if the number of flights is significantly greater for Airline 1?
 
  For instance  -> What if A1 had 400 flights and A2 had only 100 flights? 
  9.2% of 100 is not greater than 8.5% of 400. 
 
 So, we can see that (1) need not be true.  "Need not be true" .

(2) A5 with 1.2% is the smallest % among the five airlines.

But also, A5 has the least total number of flights too.
 
 So, ( lowest % among the 5 airlines ) x ( lowest absolute number of flights among the 5 airlines ) = (  least number of flights    in this category (more than 60)  among the five airlines)
 
  "Must be true".
  
 (3) Consider Airline 4.
 
 ( Lower % total delays than Airline 3 ) x ( Lower number of flights than airline 3 ) => (definitely   lesser number of total delayed flights than Airline 3  ).

So, this statement is actually not true. We can see that Airline 4 had an even lower number of total delayed flights than Airline 3. 
 
  "Need not be true" .

Hope this helps!
Harsha

Aalto700 · Answer

self-reproach:
I made careless mistake in reading "The airlines are numbered from greatest to least", I misunderstood that there are only the greast - A1, and least A5. without infor of A2, A3, A4. 
So I choose wrong answer in the part 3.

For each of 5 airlines (Airlines 1 through 5), the table shows the per

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Airline	1 to 15	16 to 30	31 to 45	46 to 60	More than 60	Total delays
	TOUR CITIES
4	6.3%	4.8%	5%	1.7%	2.5%	20.3%
3	7.5%	7.1%	4.5%	2.2%	1.7%	23%
1	8.5%	6.5%	5.8%	2.1%	1.6%	24.5%
5	8.8%	5.9%	7.1%	1.9%	1.2%	24.9%
2	9.2%	6.9%	4.9%	2.4%	2.8%	26.2%

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