The Math Beast Challenge Problem of the Week – September 10, 2012
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Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.Of three possible events, events A and B are independent, and events B and C are mutually exclusive. The probabilities that the individual events A, B, and C will occur are 0.5, 0.3, and 0.2, respectively. What is the probability that both event A and event C will occur?
The Math Beast Challenge Problem of the Week – August 27th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
At Medville Hospital, Drug X is prescribed only for Condition A and Condition B, which may occur simultaneously in the same patient. Last year, the department recorded the following statistics for prescriptions of Drug X.
Condition Number of Cases
(i.e. Number of patients with the condition)% of cases in which Drug X was prescribed A 4,000 25 B 2,000 80 Which of the following could be the number of Medville Hospital patients for whom Drug X was prescribed last year?
The Math Beast Challenge Problem of the Week – August 20th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
The volume of a chemical solution in a tank is described by the formula
, where k is a constant, T is the temperature, c is the concentration of the chemical solution, and p is the atmospheric pressure. The solution in the tank can be either hot or cold. When hot, c is half of what it is when cold, p is double what it is when cold, and T is triple what it is when cold.
If the tank can be no more than
full when hot for safety reasons, what is the maximum fraction of capacity to which the tank can be filled when the solution is cold?
, where k is a constant, T is the temperature, c is the concentration of the chemical solution, and p is the atmospheric pressure. The solution in the tank can be either hot or cold. When hot, c is half of what it is when cold, p is double what it is when cold, and T is triple what it is when cold.
full when hot for safety reasons, what is the maximum fraction of capacity to which the tank can be filled when the solution is cold?The Math Beast Challenge Problem of the Week – August 13th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
The constant rate at which machines A works is
of the constant rate at which machine B works. Under normal conditions, machine A would complete x lots in 2 days. However, when a technician attempts to use machines A and B simultaneously, there is not enough electrical power to run both machines at full power. As a result, running the machines simultaneously reduces the work rate of each machine by 20%.
How long will it take the machines to complete 3x lots, working simultaneously?
of the constant rate at which machine B works. Under normal conditions, machine A would complete x lots in 2 days. However, when a technician attempts to use machines A and B simultaneously, there is not enough electrical power to run both machines at full power. As a result, running the machines simultaneously reduces the work rate of each machine by 20%.The Math Beast Challenge Problem of the Week – August 6th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
Insurance Plan A requires the patient to pay up to the first $1,600 of any hospital bill plus 12% of the remainder of the bill. Insurance Plan B requires the patient to pay the entire amount of any hospital bill under $2,000; for hospital bills of at least $2,000, the patient pays $2,000 plus another 8% of the entire amount.
The patient would pay the same under either insurance plan for hospital bills of which of the following amounts?
The Math Beast Challenge Problem of the Week – July 30th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
x and y are positive integers such that 3x y2 = 432.
Quantity A
3xQuantity B
y2
The Math Beast Challenge Problem of the Week – July 23rd, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
A solid metal cylinder was dropped into a cylindrical glass originally holding 200Ï€ centimeters3 of water. If the metal cylinder has a radius of 3 centimeters and height of 7 centimeters, and is completely submerged in the water, by what percent did the water level in the glass rise? (Assume the metal is non-porous, so the resulting water and metal volume equals the original water volume plus the metal cylinder volume.)
The Math Beast Challenge Problem of the Week – July 9th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
y > 9
z > 2Quantity A
x2yz “ 8x2z + 3yz “ 24zQuantity B
0
The Math Beast Challenge Problem of the Week – July 2nd, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
Quantity A
The number of different ways all 9 letters in the word TENNESSEE can be arranged.
Quantity B
The number of different ways all 7 letters in the word WYOMING can be arranged.
The Math Beast Challenge Problem of the Week – June 18th, 2012
Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
The 11th grade girls at Stumpville High School have an average GPA of 3.1, and the overall 11th grade average GPA is 3.05. If all of the boys enrolled in Honors Chemistry are in the 11th grade and those boys have an average GPA of 3.8, what is the average GPA of all the 11th grade boys who are not enrolled in Honors Chemistry?