Rationale: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5
Required smallest number = 2 * 13 * 5 = 130
130 is the smallest number which should be multiplied with 520 to make it a perfect squar
The answer: (E)
Question: Find the smallest number which should be multiplied with 520 to make it a perfect square.
Options:
(A) 30
(B) 120
(C) 55
(D) 35
(E) None of these
Reasoning: Total age of students is 42X16 = 672 Years
Total age inclusive of teacher = 43X (16+1) = 731
So, Teacher's age is 731-672 = 59 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(43X1) = 59 Years
Ans: (E)
Question: The average age of a class of 42 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
(A) 30 Years
(B) 31 Years
(C) 32 Years
(D) 34 Years
(E) 59 Years
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
The answer: (B)
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
(A) 5/18
(B) 5/12
(C) 5/19
(D) 5/15
(E) 5/11
Reasoning: Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
Ans: (B)
Question: A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
Options:
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.
The answer: (A)
Question: A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
Rationale: Distance covered in first two hours = 10 Ã— 2 = 20 km
Distance covered in next two hours = 12 Ã— 2 = 24 km
Distance covered in next two hours = 14 Ã— 2 = 48 km
Distance covered in first six hours
20 + 24 + 48 = 92 km
Remaining distance = 8 km
92 + 8 = 100 km
The answer: (B)

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
Question: A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
Options:
(A) 96 km
(B) 100 km
(C) 106 km
(D) 116 km
(E) 126 km