## Solution
Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%
## What the question and answer could be
For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.
Options:
(A) 10
(B) 5
(C) 2
(D) 3
(E) 1
(C)

## Solution
One day work of A and B = 1/18
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/18 + 1/30 + 1/36
2(A + B + C) = 21/180
(A + B + C) = 13/360
Number of days required = 360/13 days.
## What the question and answer could be
A and B can do a work in 18 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
Options:
(A) 360/13 days
(B) 350/13 days
(C) 160/13 days
(D) 260/13 days
(E) 960/13 days
(A)

## Solution
Let the time taken be = x
One way distance = 45x
Total distance traveled = 2 * 45x = 90x
Total time taken = x + 2x = 3x
Average speed = 90x/3x = 30
## What the question and answer could be
A car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
(A) 30.
(B) 32.
(C) 36.
(D) 42.
(E) 44.
(A)

## Solution
He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 10 ways
Hence one chair and one table can be arranged in 10 x 10 ways = 100 ways
## What the question and answer could be
An design manager has 10patterns of chairs & 10patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 20
(B) 40
(C) 80
(D) 90
(E) 100
(E)