Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
A. 12
B. 15
C. 20
D. 24
E. 40
Assume the total members = x
Farsi = .4x
Hebrew = .75x
Farsi + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only Farsi = .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only Farsi = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 20 Only Farsi = .25*20 = 5, Only Hebrew = .6*20 = 12, both = .15*20 = 3. We have the people as whole numbers. CORRECT
D. 24
E. 40
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C