Ques: A car finishes a journey in ten hours at the speed of 65 km/hr. If the same distance is to be covered in five hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 65 km/hr
(D) 16 km/hr
(E) None of these
Ans: (C)
CoT: Distance covered by the car = 65 10 = 650 km
\ Speed = 6505 = 130 km/hr
\ Speed gain = 130 65 = 65 km/hr

Ques: Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men?
Options:
(A) 5 days
(B) 6 days
(C) 9 days
(D) 10 days
(E) None of these
Ans: (E)
CoT: 7 x 12 men complete the work in 1 day
Therefore, 1 man's 1 day's work = 1/84
7 men's 5 days work = 5/12
Remaining work = 1- 5/12 = 7/12
5 men's 1 day's work = 5/84
5/84 work is don by them in 1 day
7/12 work is done by them in ((84/5) x (7/12)) = 49/5 days = 9 4/5 days

Ques: An archer is shooting arrows from various distances. She shoots at a target from 50 yards, 60 yards, and 70 yards. The probability that she hits within the bullseye from 50 yards is 3/4, the probability that she hits within the bullseye from 60 yards is 2/3, and the probability that she hits within the bullseye from 70 yards is 3/5. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 9/10
(B) 14/15
(C) 19/20
(D) 29/30
(E) 39/40
Ans: (D)
CoT: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 50 yards)*(prob that she misses from 60 yards)*(prob that she misses from 70 yards)
Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5
Thus the probability that she misses all shots = (1/4)*(1/3)*(2/5) = 1/30
Thus the probability that she makes at least one shot = 1 - (1/30) = 29/30

Ques: If x is a positive integer, which of the following could NOT be the square of x?
Options:
(A) 5,008,644
(B) 5,004,169
(C) 4,999,696
(D) 4,995,225
(E) 4,990,752
Ans: (E)
CoT: A perfect square will never end in 2, 3, 7 or 8. (last digit cannot be 2, 3, 7 or 8)
Here E is the odd one out.