Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.
The answer: (D)
Question: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 720
(B) 1720
(C) 2880
(D) 6
(E) 10080
Reasoning: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 2
Profit to each partner = (q/2)/2 = q/4
Ans: (A)
Question: Last year, Company Z made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his two other partners. In terms of q, how much did each of the other partners receive?
Options:
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
Rationale: It's a simple geometry problem. Look at the diagram below:
The answer: (B)
Question: Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is three miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
Options:
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
Reasoning: Rate of flow of water in second hour = 24 gallons per hour
Rate of flow of water in first hour = 24/(3/2) = 16 gallons per hour
Rate of flow of water in third hour = (125/100)* 24 = (5/4) * 24 = 30 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 16+24+30 = 70 gallons
Ans: (D)
Question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 24 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
Options:
(A) 61.25
(B) 62.5
(C) 63.75
(D) 70.0
(E) 77.5
Rationale: Compound Interest: Total Balance = P(1 + R)T P = principle = starting balance = $124 R = interest rate = 4% T = time = 4 years Total balance = principle × (1 + interest rate)time = 124 × (1 + (4 / 100))4 = 145 Interest accrued = total balance - starting balance = 145 - 124 = 21
The answer: (A)
Question: Interest Rate: 4% monthly Starting Balance: 124 Time Passed: 4 months How much interest has accrued if calculated as compound interest? What is the new total balance?
Options:
(A) 21 & 145
(B) 22 & 146
(C) 23 & 145
(D) 20 & 140
(E) None
Rationale: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
The answer: (E)

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: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32