If a v b means ab + 1 and a @ b means a + b, then evaluate
Number Sense and Logical Reasoning
Defined Operation 2; 5 Parts
The operation x,y is defined by x,y = (x + 1)(y + 1) – 1 = xy + x + y. Which of these statements is false?
- x,y = y,x for all real x and y.
- x,(y + z) = (x,y) + (x,z) for all real x, y, and z.
- (x – 1),(x + 1) = (x,x) – 1 for all real x and y.
- x,0 = x for all real x.
- x,(y,z) = (x,y),z for all real x, y, and z.
Defined Operation; Find Formula
If 4 → 3, 10 → 6, 7 → 4.5, then what is the formula for x → ?
Defined Operation; Do Inverse
Suppose a linear operation �/� is defined so that:
5 / = 11;
8 / = 17;
12 / = 25.
What is n if n / = 35?
Defined Operations 1; Do Composition
Suppose the operations “#” and “t” are defined so that:
6 # = 20; 2 # = 4; 10 # = 36; and 5 t = 4.5; 10 t = 7; 8 t = 6.
Then what is n if 3 # # t = n?
Kumquat House Numbers
A new housing development, Mango Manors, is being built outside of town. It costs five cents to buy a single digit house number, but two digits can be bought for nine cents. If each home owner on Kumquat Street, a street with only single digit and 2-digit house numbers, buys the numbers for his own house, the total amount paid is $2.15. If one person buys them all, then the total amount paid is $2.12. How many single digit house numbers are on Kumquat Street?
- 3
- 4
- 5
- 6
- 7
Euler Fortune
A father leaves at his death several children who share in his property in the following manner:
- The first child receives 100 crowns and a tenth part of what remains.
- The second child receives 200 crowns and a tenth part of what remains.
- The third child receives 300 crowns and a tenth part of what remains.
- And so on.
Now, it is found in the end that the property has been divided equally among all the children. How much was the fortune, how many children were there, and how much did each child receive?
Supermarket, Apples
The Superduper Supermarket has 128 crates of apples that have just arrived at the loading dock. Each crate contains at least 120 apples and at most 144 apples. What is the largest integer n you can find such that there must be at least n crates containing the same number of apples? (This means that, even if you make the number of apples in each crate as different as you can possibly make them, there are still going to be n crates with the same number of apples.)
- 4
- 5
- 6
- 24
- 25
Kite Strings
Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?
Garden Crops
A large organic nursery has somewhere between 3 and 6 (inclusive) garden plots of herbs when it closes for the season in the fall. In each plot there are between 20 and 30 (inclusive) rosemary plants. If, typically, 10% of those plants don’t winter over successfully until spring, what would be the largest number of plants that could be lost during the winter?