## Negation, Kmart Barbells

If the statement “All sets of barbells in Kmart are on sale” is false, then which of the following statements must be true?

1. All sets of barbells in Kmart are not on sale.
2. There is some set of barbells in Kmart that is not on sale.
3. No set of barbells in Kmart is on sale.
4. Not all sets of barbells in Kmart are on sale.
1. II only
2. IV only
3. I and III only
4. II and IV only
5. I, II, and IV only

## Barber Pole

The revolving portion of a splendid barber pole is a cylinder 4 feet tall and 6 inches in radius. The red stripe is painted in a spiral around the cylinder and makes exactly 8 complete turns around it from bottom to top. How long is the stripe? (Ignore its width.)

## Points on Line Segment

Points P and Q are on line segment AB, and both points are on the same side of the midpoint M of AB. Point P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ = 2, then what is the length of AB?

In the barnyard there are some cows and some chickens. When asked to count them, Marty came back and said that the number of legs, total, was 84 more than twice the number of heads. So how many of each kind of animal are there?

Cosima is in the business of importing hand-loomed Guatemalan shirts for the Fair Trade gift shop in town. The shirts cost her a certain amount, and her profit, when she sells them to the gift shop, is x% of what they cost her. (Then the gift shop marks the price up some more and sells them to the public, but that isn’t relevant.)

Cosima has now found a second source of shirts, from Peru. These cost her 8% less than the shirts from Guatemala. She sells the Peruvian shirts to the gift shop at the same price as the Guatemalan shirts, and because they cost her less, her rate of profit is higher: (x + 10)%. This information is enough for you to figure out what x is.

## Arithmetic Mean & Geometric Mean

If the arithmetic mean of x and y is double their geometric mean, with x > y > 0, then a possible value for the ratio x/y, to the nearest integer, is:

1. 5
2. 8
3. 11
4. 14
5. none of these.