question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
Options:
(A) 99
(B) 98
(C) 97
(D) 96 answer
(E) 95
answer: Stream of consciousness: The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this. The answer is (D).


q: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 22 sec
(B) 16 sec
(C) 17 sec
(D) 88 sec
(E) 20 sec
a: Stream of consciousness: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec The answer is (E).


question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long?
Options:
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 162 sec
(D) 244 sec
(E) 2 mins 44 sec
answer: Stream of consciousness: D = 25 * 60 + 1200 = 2700 m
T = 2700/60 * 18/5 = 162 se The answer is (C).


q: The average of 7 consecutive numbers is 33. The highest of these numbers is:
Options:
(A) 28
(B) 30
(C) 33
(D) 36
(E) 28
a: Stream of consciousness: The average of 7 consecutive numbers will be the 4th number which is given to be = 33 5th number = 34, 6th number = 35, 7th number = 36 The answer is (D).


question: A car finishes a journey in five hours at the speed of 100 km/hr. If the same distance is to be covered in two hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 150 km/hr
(D) 16 km/hr
(E) None of these
answer: Stream of consciousness: Distance covered by the car = 100 × 5 = 500 km
\ Speed = 500⁄2 = 250 km/hr
\ Speed gain = 250 – 100 = 150 km/hr The answer is (C).


question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
(A) 5%
(B) 10%
(C) 25%
(D) 40%
(E) 55%
answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: Assuming that the technician makes a round-trip of 40 miles (each way is 20 miles), then the technician would have completed 20 miles + 2 miles (10% of the remaining 20 miles). Therefore, the total is 22 miles. 22miles/40 miles is 55% of the entire trip. The answer is (E).