Members of a certain group of airline pilots fly only Boeing and Airbu

Question

Members of a certain group of airline pilots fly only Boeing and Airbus airplanes. A total of 25 of the pilots fly Boeing airplanes, and 75 of the pilots fly Airbus airplanes.

In the table, select two numbers that are consistent with the information given. In the first column, select the row that displays the largest number of pilots in the group who fly either Boeing or Airbus airplanes. In the second column, select the row that displays the largest number of pilots in the group who possibly could be flying both Boeing and Airbus airplanes. Select only one option in each column.

p456 · Accepted Answer

90, 25

I feel this is a trap question. Question asked   LARGEST  , so i am not going by the rules of equation( A or B = A + B - Both)

1. Fly either Boeing or Airbus

largest number of pilots who "Fly either Boeing or Airbus" = 75 + 25 = 100
100 not there in options, next largest is  90 .

2. Fly both Boeing and Airbus

largest number of pilots who "Fly both Boeing and Airbus" = min(75,25) =  25

Elite097 · Answer

Fly either Boeing and Airbus:
Max who fly either =75+25=100
The number right below 100 is 90 among answer choices hence 90

Fly both Boeing and Airbus 
Max that fly both =25.
Largest number =25

pintukr · Answer

Members of a certain group of airline pilots fly only Boeing and Airbus airplanes. A total of 25 of the pilots fly Boeing airplanes, and 75 of the pilots fly Airbus airplanes.

In the table, select two numbers that are consistent with the information given. In the first column, select the row that displays the largest number of pilots in the group who fly either Boeing or Airbus airplanes. In the second column, select the row that displays the largest number of pilots in the group who possibly could be flying both Boeing and Airbus airplanes. Select only one option in each column.

As per the given data in the stimulus,

MAX possible number of pilots in the group who fly either Boeing or Airbus airplanes = 75 + 25 = 100 (with no pilot as flying both)
MIN possible number of pilots in the group who fly either Boeing or Airbus airplanes = 75 + 25 - 25= 75 (with 25 pilots as flying both)

ie, 75 <= (Either) <=100

MAX possible number of pilots in the group who possibly could be flying both Boeing and Airbus airplanes = 25
MIN possible number of pilots in the group who possibly could be flying both Boeing and Airbus airplanes = 0

ie, 0 <= (Both) <= 25

Only figures 90 and 10 satisfy both the criteria
(Possible for Boeing = 25, Airbus = 75 and Both = 10;

so, Either Boeing or Airbus = 25 + 75 - 10 = 90)

So, 
  Fly either Boeing or Airbus = 90
Fly both Boeing and Airbus = 10

hallfootball · Answer

Let number of pilots flying Airbus = a
Let number of pilots flying Boeing = b
Let number of pilots flying both Airbus and Boeing = c
a, b and c are non negative integers.

A total of 25 of the pilots fly Boeing airplanes
i.e. a + c = 25, let's call this equation 1

A total of 75 of the pilots fly Airbus airplanes
i.e. b + c = 75, let's call this equation 2

Adding equation 1 and 2 we get: a + b + 2c = 100, let's call this equation 3.

Column 1: largest number of pilots in the group who fly either Boeing or Airbus airplanes

i.e. we need to maximize a + b

From equation 3: a + b = 100 - 2c
To maximize a + c we need to minimize b
The maximum value a + b can take is 100.

As 100 is not one of the options we need another constraint for the answer.
Looking at the value of a + b we see that a + b = Even - Even = Even. (because 2c is even)

That means we are left with 2 options a + b = 10 or a + b = 90
a + b cannot be 10 because that would violate equation 1 where c needs to take a value between 65 and 75 as per equation 2, which will not satisfy equation 1.

Hence a + c = 90 from the given option choices.

Column 2: the largest number of pilots in the group who possibly could be flying both Boeing and Airbus airplanes.

We need to maximize c

From equation 3 we can get the following: c = 50 - (( a+ b) / 2)
Hence the maximum value c can take is 50.
This eliminates 2 option choices (90 and 110)

And the next biggest value c can take is 29.

Hence c = 29 from the given option choices.

Sajjad1994 · Answer

Official Explanation

The correct answers are 90 pilots in the group who fly either Boeing or Airbus airplanes and 25 pilots in the group who fly both Boeing and Airbus airplanes.

There are 25 pilots who fly Boeing airplanes, and 75 pilots who fly Airbus airplanes. Therefore, if none of the pilots fly both types of airplanes, then 100 pilots in the group fly either Boeing or Airbus airplanes. The number 100 is not included in the table, and 110 is too large, so the largest number of pilots listed in the table who fly either Boeing or Airbus airplanes is 90.

If all of the pilots who fly Boeing airplanes also fly Airbus airplanes, then 25 pilots in the group would fly both Boeing and Airbus airplanes. The number 25 is given in the table, so 25 is the largest number of pilots in the group flying both types of planes.

pizzapalooza · Answer

Other options apart from 90 are also not valid.
For eg) If I try the next biggest number after 90 i.e. 29,
A or B = A + B - both
29 = 75 + 25 - both, which makes both 71 (Not possible since overlap can be max 25)

Members of a certain group of airline pilots fly only Boeing and Airbu

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Fly either Boeing and Airbus	Fly both Boeing and Airbus
		10
		25
		27
		29
		90
		110

GMAT Two-part Analysis (TPA) Questions

Members of a certain group of airline pilots fly only Boeing and Airbu

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

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My Rewards