Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
The answer: (D)
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options:
(A) 22 1/8 %
(B) 22 3/2 %
(C) 28 1/2 %
(D) 22 1/2 %
(E) 32 1/2 %
Reasoning: Total work done by both machines in a minute = 15 + 10 = 25 copies
Total number of copies required = 1000
Time = 1000/25 = 40 mins
Ans: (C)
Question: One copy machine can make 15 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 1,000 copies?
Options:
(A) 20 minutes
(B) 30 minutes
(C) 40 minutes
(D) 50 minutes
(E) 60 minutes
Rationale: Each side is p/2
A = (p/2)^2 = (p^2)/4
The answer: (E)
Question: What is the area of a square with perimeter 2P ?
Options:
(A) 16p^2
(B) 4P
(C) P^2/5
(D) P/16
(E) P^2/4
Reasoning: There are 35 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 35 ways. When one person is appointed as leader, we are left with 35 students. Out of these 34 teachers, we can select one class representative. So, a class representative can be selected in 34 ways. Hence, the number of ways in which a leader and class representative can be selected = 35 x 34 = 1190
Ans: (D)
Question: From among the 35 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1190
(E) 1460
Rationale: The integer should be divisible by: 12, 13, 14, 15 and 16, that is 3*2^2, 13, 2*7, 3*5 and 2^4. The least common multiple of these integers is the product of 13, 7, 5, 3 and 2^4. Then, R/13 is (13 * 7 * 5 * 3 * 2^4)/13 = 7*5*3*16 = 1680.
The answer: (C)
Question: If R is the least positive integer that is divisible by every integer from 12 to 16 inclusive, then R/13 is =
Options:
(A) 40320
(B) 21840
(C) 1680
(D) 840
(E) 240
Rationale: 125^10 = (5^3)^10 = 5^30
The answer: (E)
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30