Assignment 1



ENGR 300

QUIZ 3

1. A person tells you that he will be 76 years old in the year x2, where x is a counting number. In what year was he born?

2. The same person in problem one graduated from high school in the year that satisfies these conditions: (1) The sum of the digits is 23; (2) The hundreds digit is 3 more than the tens digit; (3) No digit is an 8. In what year did he graduate?

3. There is a two-digit number between 20 and 30 such that the sum of the cubes of its digits is equal to three times the number. What is the number?

4. Eve said to Adam, “If you give me one dollar, then we will have the same amount of money.” Adam then replied, “Eve, if you give me one dollar, I will have double the amount of money you are left with.” How much does each have?

5. The number of hens and cows in a barnyard adds up to 11. The number of legs among them is 32. How many hens and how many cows are in the barnyard? (There are no handicapped)

6. A person must take a wolf, a goat, and some cabbage across a river. The rowboat to be used has room for the person plus either the wolf, the goat, or the cabbage. If the person takes the cabbage in the boat, the wolf will eat the goat. While the wolf crosses in the boat, the goat will eat the cabbage. The goat and cabbage are safe only when the person is present. Even so, the person gets everything across the river. Explain how.

7. You have eight coins. Seven are genuine and one is a fake, which weighs a little less than the other seven. You have a balance scale, which you may use only three times. Tell how to locate the bad coin in three weighing. Then show how to detect the bad coin in only two weighing.

8. Three women, Ms. Thompson, Ms. Johnson, and Ms. Andersen, are sitting side by side at a meeting. Ms. Thompson always tells the truth, Ms. Johnson sometimes tells the truth, Ms. Andersen never tells the truth. The woman on the left says, “Ms. Thompson is in the middle.” The woman in the middle says, “I’m Ms. Johnson,” while the woman on the right says, “Ms. Andersen is in the middle.” What are the correct positions of the women?

9. Only one of the numbers here is a perfect square. Which is it?

(No calculator is needed)

a) 23,784,855,888,784

b) (b) 49,552,384,781,228

c) (c) 33,587,988,047,112

d) (d) 4,987,237,011,667

10. In how many different ways can you make change for a half dollar using currently minted U.S. coins, if pennies are not allowed?

11. In Farmer Jack’s will, he left 1/2 of his horses to his son John, 1/3 to his daughter Linda, and 1/9 to his son Jeff. Jack had 17 horses, so how were they to comply with the terms of the will? The attorney came to their rescue and was able to execute the will to the satisfaction of all. The attorney added one of his own horses to the 17, giving a total of 18. John received 9, Linda received 6, and Jeff received 2. The attorney then took back his horse and everyone was happy. Were the terms of the will actually fulfilled?

12. In 1980, the defense budget of a certain country was $30 million out of a total budget of $500 million. In 1981, the defense budget of that same country was $35 million out of a total budget of $605 million. The country’s inflation rate for that one-year period was 10%.

(a) Use the facts to argue that the defense budget increased from 1980 to 1981.

(b) Use the facts to argue that the defense budget declined from 1980 to 1981.

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