A maid was about to wipe the crumbs off a rectangular table measuring 4 ft. by 8 ft. when the butler, a methodical type, took over. “You need a system!” he said. They both had very short arms and could only reach 2 feet with the dust cloth, so the butler decided to get all the crumbs together at center point C along one side. He walked along the opposite side, AB, pushing all the crumbs as far as he could directly toward C, and then did the same thing walking down each end; finally he went to the other long side to pull everything toward the dustpan. When he finished, the maid complained. Why?

## Geometry

## Tangalese People Non-Toxic

The following three statements are true:

Tangalese people are non-toxic.

No person is a dingbat who can dance the hustle.

Non-toxic persons are dingbats.

Which of the following are true?

- Dingbats are Tangalese.
- Some Tangalese can dance the hustle.
- A person who cannot dance the hustle is toxic.
- No Tangalese person can dance the hustle.

## Pickled Walnuts, Prof. Piltdown

On the assumption the following nine statements are factually correct, what conclusion, if any, can be drawn?

- Pickled walnuts are always provided at Professor Piltdown’s parties.
- No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
- All armadillos can speak the Basque dialect.
- No animal can be registered as a philatelist who does not carry a collapsible umbrella.
- Any animal that can speak Basque is eligible for the Tintinnabulum Club.
- Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
- All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
- The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s.
- Only animals that take taxis in Bond Street carry collapsible umbrellas.

## True Statements on Card

Here is a card with the four statements that you see, and no others. Assume that each statement on the card is either true or false; then find and identify each false statement. (Refer to them as a, b, c, d if you want, to speed things up.)

On this card exactly two statements are true.

On this card exactly three statements are true.

On this card exactly four statements are true.

## 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?

- All sets of barbells in Kmart are not on sale.
- There is some set of barbells in Kmart that is not on sale.
- No set of barbells in Kmart is on sale.
- Not all sets of barbells in Kmart are on sale.

- II only
- IV only
- I and III only
- II and IV only
- I, II, and IV only

## Volume Equals Surface Area

The number of cubic feet in the volume of a cube is the same as the number of square inches in its surface area. The length of the edge in feet is:

- 6
- 864
- 1728
- 6 · 1728
- 2304

## Barrels Partially Filled

Of two identical barrels, one is half full and one is two-thirds full. One quarter of the liquid in the second barrel is poured into the first. The first barrel now contains 25 more gallons of liquid than the second. Find the capacity in gallons of one of the barrels.

## Tennis Ball Can Volume

In a can of tennis balls that is exactly three balls high, which is greater, the volume of the balls or the volume of the air around the balls? (Disregard the thickness of the balls.)

## Humber Bridge, Radius of Earth

The single-span suspension bridge crossing the estuary of the Humber River on the east coast of England has towers that are 162.5 meters tall (AC=BD). The span at sea level is 1410 meters (about 4/5 of a mile). The tops of the towers are 3.6 cm farther apart than the bases (i.e. AB=1410.036 m). What is the radius of the earth?

## Geometric Mean in Parallelogram

Given parallelogram ABCD with its diagonals drawn. A line through B intersects AC at E, DC at G, and line AD at F. Observe that △AEF is similar to △CEB, and show that EB is the geometric mean of EG and EF.