Suppose that Amtrak has trains leaving from Washington to New York City and also from New York City to Washington every hour on the hour. Also suppose that the trip from one city to the other takes 4.5 hours and all trains travel at the same speed. If you are on the train from DC to NYC, how many trains going the other way will you pass?
Set 17
Mixed Tennis Team
A mixed tennis team of 12 persons has one-third women and two-thirds men. What is the smallest number of additional people that should be recruited for the team so that the team as a whole is 20% women?
Strange Equation
Gear Wheels, Small
The marks on the faces of these gears are aligned as shown. What is the least number of turns that gear A must make so that the marks are all re-aligned as shown?
Phony Product (x – a)(x-b)…(x-z)
What is this product? (x – a)(x – b)(x – c)(x – d) . . . (x – z)
Sum of Odd #s is the Squares 1
- What does picture A have to do with picture B?
- Continue both A and B for two more steps.
- Find the totals in A. What kind of numbers are they?
- Does B tell you why these numbers are what they are? Explain.
- What is 1 + 3 + 5 + 7 + . . . + 99?
Parentheses Insert
Insert parentheses to make the following equation true:
2 · 1 + 2 · 3 – 2 · 2 – 1 = 12
Cows and Oxen Cost
John spent $1705 on cows and oxen. Cows cost $40 and oxen cost $75 each. He bought twice as many cows as oxen. How many of each did he buy?
Bananas and Pears
Simon was sent out to buy some fruit, and he came back with 3 bananas and a half-dozen pears. When his mother asked what he had paid, however, the boy wasn’t quite sure.
“I know that each banana cost one cent more than the price of a pear,” he said, “and I noticed that what I paid for the pears was the same as I paid for the bananas but reversed.”
His mother couldn’t quite follow this: “What do you mean by reversed?” she asked him.
“Well, I paid less than a dollar for each little lot,” replied Simon, “and the amounts for the two lots were the same figures, but for one lot they were the other way around.”
This was even more confusing than before. But perhaps you can see how much Simon paid altogether.
Square is Cube (Locker Number)
What’s Graziano’s locker number at the gym? It’s a three-digit perfect square and also a perfect cube.