What is the sum of all even integers between 30 and 50, inclusive?
Answer(s): D
The sum of the even integers between 30 and 50 inclusive can be calculated using the product of the number of integers by their average. The average of a fixed-difference sequence of numbers can be calculated as the average of the largest and the smallest numbers: . We remember that between 30 and 49, inclusive, there are 20 numbers of which half are even and half odd. Add 1 (the number 50) to the 10 even numbers to receive a total of 11 even integers, multiply it by the average to get the sum: .
The price (p) of product X depends on the yearly number of units produced (n) according to the following formula: p= . What will the estimated price per unit be next year if an estimated number of 260 units will be sold?
Answer(s): A
Plug the number of units into the given formula to find the price per unit: .
John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
Answer(s): C
The leftmost book is a mathematics book; the next is physics and so on. So, the odd places books are the mathematics books and the even placed books are the physics books. The mission is therefore, arranging three mathematics books in three places (3! =6 arrangements) and three physics books in three places (3! =6 arrangements). The total number of different arrangements is the product of the two missions:
An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?
Answer(s): B
The combined return is 7% of $30,000 = $2,100. Subtract the 6% return on his $10,000 investment = $600. $2,100-$600=$1,500. This is the return on his second investment of $20,000. $1,500 of $20,000 is a 7.5% return.
What is the probability of getting an identical result on three consecutive tosses of a coin?
The first toss will be either heads or tails. The probability that the result on the second toss is identical to the first is 1/2. The probability that the result on the third toss is identical to that of the second is also 1/2. The total probability is, therefore, .
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