Question
In a survey of 100 MBA aspirants: 55 prepare for
SNAP 50 prepare for CAT 45 prepare for XAT 25 prepare for both SNAP and CAT 20 prepare for both CAT and XAT 15 prepare for both SNAP and XAT 10 prepare for all three exams. How many students prepare for exactly one exam?Solution
ATQ, Let S, C, X denote sets of students preparing for SNAP, CAT, XAT. Given: |S| = 55, |C| = 50, |X| = 45 |S ∩ C| = 25, |C ∩ X| = 20, |S ∩ X| = 15 |S ∩ C ∩ X| = 10 First, find those in exactly two sets: Exactly S∩C only = 25 − 10 = 15 Exactly C∩X only = 20 − 10 = 10 Exactly S∩X only = 15 − 10 = 5 Now, those only in a single set: Only S = 55 − (15 + 5 + 10) = 55 − 30 = 25 Only C = 50 − (15 + 10 + 10) = 50 − 35 = 15 Only X = 45 − (10 + 5 + 10) = 45 − 25 = 20 Total with exactly one exam = 25 + 15 + 20 = 60. (Check: Total in at least one = 60 (exactly one) + 30 (exactly two) + 10 (all three) = 100.)
This one act of kindness ___________ all the wrong doings that he has ever done.           Â
These telemarketers have been calling me ___________, even though I said I was not interested in their product.
This cream helps _________ the skin from harmful radiation from the sun.
The child agreed to have food, ________ reluctantly, when his mother said they were going to the park.
His concentration is very weak and his mind gets filled with ___________ thoughts after reading mere five words.
Steve Jobs is the legendary ___________ of Apple.
Many people realized that the pill was just a vitamin tablet and what really changed their disease was the _________.
Given his grandmother’s health condition, he’ll now have to ___________ money for a full-time nurse.
The opinions of the state and central governments were ____________ on the new policy.
The small businesses continued to face ________ with decrease in demand during the lockdown.
