Problem Solving

For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation (a , b , c) Θ (d , e , f) = a d + b e + c f . What is the value of (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) ?

A sequence of numbers a 1 , a 2 , a 3 ,.... is defined as follows: a 1 = 3 , a 2 = 5 , and every term in the sequence after a 2 is the product of all terms in the sequence preceding it, e.g, a 3 = (a 1) (a 2) and a 4 = (a 1) (a 2) (a 3) . If a n = t and n > 2 , what is the value of a n + 2 in terms of t?

Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

If n = 33 43 + 43 33 what is the units digit of n?

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

If S = 1 + 1 2 + 1 3 2 + 1 4 2 + 1 5 2 + 1 6 2 + 1 7 2 + 1 8 2 + 1 9 2 + 1 10 2 , which of the following is true?

At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?

If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?

In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?

To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

What is the value of √ 17 + √ 47 17 − √ + 47 − √ , to the nearest whole number?

If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b =

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

2018.OG.05.055.q.png [ 56.01 KiB | Viewed 60823 times ] According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D?

m ⊕ p = n ⊕ r = m n ⊕ q = q p ⊕ q = p q ⊕ p = r If the relations shown hold for the operation ⊕ and the numbers m, n, p, q, and r, then [ (m ⊕ p) ⊕ q ] ⊕ p =

The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?

The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

If x(2x + 1) = 0 and (x + 1/2)(2x - 3) = 0, then x =