Bunuel wrote:

GRE Multiple Answer Challenge Question

A space program is recruiting a team of astronauts to journey to Mars aboard a four-person shuttle. If the number of possible teams is less than 100 but greater than 10, then what is the possible number of astronauts who did not make the space team? Indicate all such numbers.

[A] 9

[B] 8

[C] 7

[D] 6

[E] 5

[F] 4

[G] 3

[H] 2

[I] 1

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solution.

Now here the total number of astronount choosen is not given, let it be = x

now we have to choose 4 astronount from the x astronounts

i.e, we can re write as xC4 and that has to be between 10 and 100

Now if x= 5 then the value becomes = 5 (5C4)

if we choose x=6 then the value becomes = 15 (6C4)

if we choose x= 8 then the value becomes =70 (8C4)

if we choose x= 9 then value becomes = 126 (9C4)

therefore it should lie between 6 and 8 .

Now we need the astronauts who did not meet i.e we have to subtract 4 from the total numbers

i.e 6-4 =2 and 8-4 = 4 (minimum and maximum values)

Therefore numbers 2 ,3, 4 did not made it.

Kindly let me know if my reasoning is correct

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