Crumbs on a Table

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?

Triangle Rotating in Square

Equilateral triangle EKP with side EK of length 2 inches is placed inside square EAMI with side of length 4 inches so that K is on side EA. The triangle is rotated clockwise about K, then P, and so on along the sides of the square until E, K, and P return to their original positions. The length of the path in inches traversed by vertex P is equal to:

1. 20/3
2. 32/3
3. 12
4. 40/3
5. 15

Mongoes Eat Booms

Suppose that each of the following statements is true:

If mongoes eat booms, then mongoes are dangerous.
Either flems are tall or mongoes are not dangerous.
Flems are not tall.

Which of the following conclusions must also be true?

1. Mongoes eat booms.
2. Mongoes do not eat booms.
3. Flems are not dangerous.
4. Mongoes are dangerous.
5. None of these statements is a possible conclusion.

Subsistence Allowance, Passport

A notice goes up on the company bulletin board:

“All those who have not already received their subsistence allowance this week should report to the Deputy Assistant Bursar (D.A.B.) at 9 am next Monday, unless they also failed to get it last week, in which case they should not report to anybody anywhere, unless they are over 21 and/or have a maternal grandmother who is still alive, in which case they should either report to the Substantive Acting Registrar at 10 pm on Tuesday or to the D.A.B. at 12 noon on Wednesday according to whether their surname begins with a letter in the first half of the alphabet or not, unless their paternal grandmother does not have or did not have a passport, in which case they should report to the Warden as soon as possible, unless they have already passed their driving test and/or do not have a bicycle, in which case they should take a couple of aspirins and go quietly home to bed.”

Ms. Zola Hooberry, age 20, has not received her subsistence allowance this week or last. She has a bicycle but has not passed her driving test. Both her grandmothers are still alive and have passports.

What should she do?

Pickled Walnuts, Prof. Piltdown

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

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

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?

1. Dingbats are Tangalese.
2. Some Tangalese can dance the hustle.
3. A person who cannot dance the hustle is toxic.
4. No Tangalese person can dance the hustle.

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 one statement is true.
On this card exactly two statements are true.
On this card exactly three statements are true.
On this card exactly four statements are true.

Yaks, Blats, and Blobs

Given the two hypotheses:

1. Some yaks are not blats and
2. No blats are blobs,

if “some” means “at least one,” we can conclude that:

1. Some yaks are not blobs.
2. Some blobs are not yaks.
3. No yak is a blob.
4. Some yaks are blobs.
5. I, II, III, and IV are not deducible from the given statements.