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

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

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.

Hello Everyone!

You guys are doing great in this competition.

OA to this question is:

Fly either Boeing or Airbus = 90
Fly both Boeing and Airbus = 25

Official explanation is also posted.

You are doing great as well Sajjad1994. To get us the questions on a section, which is completely unknown is just fantastic. We all are learning together.