Deck 1: The Nature of Problem Solving

Question 1

Compute the result. Leave your answer in scientific notation. Round your answer to 1 decimal place.
​

Answer 1

Question 2

If a country's annual production of sugar is 39,000,000 tons, estimate the number of grains of sugar produced in a year in that country. Use scientific notation. Round your answer to 4 decimal places. (Note: There are 2,000 lb per ton. Assume there are 2,260,000 grains in a pound of sugar.)

Answer 2

Question 3

Write the number in fixed-point notation.
​

Answer 3

407,000

Question 4

Write the number in fixed-point notation. Round your answer to 10 decimal places. ​ ​

A) 0.0771604938
B) 0.0000007716
C) 0.0077160494
D) 0.6666666667
E) 0.0007716049

Question 5

Compute the result. Leave your answer in scientific notation.
​

Question 6

Compute the result. Leave your answer in scientific notation. Round your answer to 1 decimal place. ​ ​

A)
B)
C)
D)
E) ​

Question 7

Express the number in scientific notation and in floating-point notation. ​
68
​

A) Scientific notation:
Floating point notation: 6800 05
B) Scientific notation:
Floating point notation: 68 02
C) Scientific notation:
Floating point notation: 0.68 07
D) Scientific notation:
Floating point notation: 6.8 03
E) Scientific notation:
Floating point notation: 6.8 03

Question 8

Compute the result. Leave your answer in scientific notation. Round your answer to 1 decimal place. ​ ​

A)
B)
C)
D)
E)

Question 9

Compute the result. Leave your answer in scientific notation.
​

Question 10

Write the number in fixed-point notation. ​ ​

A) 804,000
B) 8,040,000
C) 80,400
D) 80,400,000
E) 8,040,000,000

Question 11

Imagine that you have written down the numbers from 1 to 1,000. What is the total number of zeros you have recorded? ​

A) 161
B) 71
C) 191
D) 192
E) 141

Question 12

If it takes one second to write down each digit, how long will it take to write down all the numbers from 1 to 1,000? ​

A) 48 min, 13 sec.
B) 105 min, 1 sec.
C) 91 min, 3 sec.
D) 48 min
E) 83 min, 6 sec.

Question 13

Write the number 2,600 in scientific notation and in floating-point notation (as on a calculator). Round your answers to 1 decimal place.
​
Enter the number in scientific notation. __________
​
The number in floating-point notation is __________ __________.

Question 14

Imagine that you have written down the numbers from 1 to 300. What is the total number of zeros you have recorded?
​
__________ zeros

Question 15

Write the number in fixed-point notation. Write your answer as a circulating fraction. Round your answer to 3 decimal places.

Question 16

Compute the result. ​ ​

A)
B)
C)
D)
E)

Question 17

How many pages are necessary to make 1,650 copies of a manuscript that is 487 pages long? (Print on one side only.)
​
__________ pages

Question 18

If it takes one second to write down each digit, how long will it take to write down all the numbers from 1 to 1,100?
​
It takes __________ min, __________ sec.

Question 19

How many pages are necessary to make 1,050 copies of a manuscript that is 423 pages long? (Print on one side only.) ​

A) 915,850
B) 775,850
C) 626,650
D) 423
E) 444,150

Question 20

If a country's annual production of sugar is 30,000,000 tons, estimate the number of grains of sugar produced in a year in that country. Use scientific notation. Round your answer to 4 decimal places. (Note: There are 2,000 lb per ton. Assume there are 2,260,000 grains in a pound of sugar.) ​

A)
B)
C)
D)
E)

Question 21

Perform the operations.
​

Question 22

If a family has 7 children, in how many ways could the parents have 3 boys and 4 girls as children? ​

A) 7
B) 38
C) 3
D) 40
E) 35

Question 23

Use Euler circles to check the validity of the argument. ​
No politicians are honest. Some dishonest people are found out. Therefore, some politicians are found out.
​
The argument is __________.
​

A) not valid
B) valid

Question 24

Use Euler circles to check the validity of the argument. ​
All lions are fierce. Some lions do not drink coffee. Therefore, some creatures that drink coffee are not fierce.
​
The argument is __________.
​

A) not valid
B) valid

Question 25

Perform the operations. ​ ​

A) 33
B) 39
C) 36
D) 37
E) 300

Question 26

What is the sum of the first 80 consecutive odd numbers? ​

A) 6,396
B) 6,404
C) 6,360
D) 6,400
E) 6,480

Question 27

Find the seven pattern. ​

A) 7, 5, 3, 1, 8, 7, 5, 3, 9, . . .
B) 7, 6, 4, 2, 7, 7, 5, 3, 8, . . .
C) 7, 6, 3, 2, 8, 7, 4, 3, 9, . . .
D) 7, 5, 3, 1, 8, 6, 4, 2, 9, . . .
E) 7, 5, 4, 1, 7, 6, 5, 2, 8, . . .

Question 28

12 full crates of walnuts weigh 414 pounds, whereas an empty crate weighs 7 pounds. How much do the walnuts alone weigh? ​

A) 407 pounds
B) 402 pounds
C) 330 pounds
D) 421 pounds
E) 323 pounds

Question 29

Perform the operations.
​

Question 30

How many 9-cent stamps are there in a dozen? ​

A) 10
B) 108
C) 9
D) 12
E) 3

Question 31

Perform the operations. ​
6 + 8 × 5
​

A) 49
B) 70
C) 46
D) 43
E) 40

Question 32

Perform the operations. ​ ​

A) 80
B) 86
C) 83
D) 74
E) 40

Question 33

Alex, Beverly, and Cal live on the same straight road. Alex lives 13 miles from Beverly and Cal lives 2 miles from Beverly. How far does Alex live from Cal? ​

A) 15 miles
B) 11 miles
C) 11 miles or 15 miles
D) 13 miles or 2 miles
E) 24 miles or 17 miles

Question 34

Consider the pattern:
​
9 × 1
-
1
=
8
9 × 21
-
1
=
188
9 × 321
-
1
=
2888
9 × 4321
-
1
=
38888
​
Use this pattern to find .

Question 35

If an island's only residents are penguins and bears, and if there are 16 heads and 38 feet on the island, how many penguins and how many bears are on the island? ​

A) 12 bears, 4 penguins
B) 11 bears, 5 penguins
C) 13 bears, 3 penguins
D) 4 bears, 12 penguins
E) 3 bears, 13 penguins

Question 36

Consider the pattern:
​
123456789
×
9
=
1111111101
123456789
×
18
=
2222222202
123456789
×
27
=
3333333303
​
Use this pattern to find .

Question 37

Perform the operations.
​ ​

Question 38

Use Euler circles to check the validity of the argument. ​
All candy is fattening. All candy is delicious. Therefore, all fattening food is delicious.
​
The argument is __________.
​

A) not valid
B) valid

Question 39

Find the first five terms of the seven pattern.

Question 40

What is the sum of the first 100 consecutive odd numbers?

Question 41

If posts are spaced 11 feet apart, how many posts are needed for 99 feet of straight-line fence?
​
__________ posts
​

Question 42

If posts are spaced 14 feet apart, how many posts are needed for 98 feet of straight-line fence? ​

A) 22 posts
B) 8 posts
C) 98 posts
D) 7 posts
E) 9 posts

Question 43

If a family has 4 children, in how many ways could the parents have 2 boys and 2 girls as children?
​
__________ ways
​

Question 44

There are four separate, equal-size boxes, and inside each box there are two separate small boxes, and inside each of the small boxes there are three even smaller boxes. How many boxes are there all together?
​
__________ boxes
​

Question 45

If an island's only residents are penguins and bears, and if there are 17 heads and 38 feet on the island, how many penguins and how many bears are on the island?
​
The number of bears is __________.
​
The number of penguins is __________.
​

Question 46

Ten full crates of walnuts weigh 390 pounds, whereas an empty crate weighs 5 pounds. How much do the walnuts alone weigh?
​
__________ pounds
​

Question 47

Alex, Beverly, and Cal live on the same straight road. Alex lives 9 miles from Beverly and Cal lives 4 miles from Beverly. How far does Alex live from Cal?
​
If there is more than one answer, separate them with commas.
​

Question 48

Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground (see figure below). It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1,006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, "If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the rope's length by a foot. How can Ahmes reach the central ankh tower and touch it?
​ ​
Ahmes' dilemma. Note that there are two ankh-shaped towers. One stands on a cylindrical platform in the center of the funnel. The platform's surface is at ground level. The distance from the platform surface to the liquid is 500 ft. The other ankh tower is on land, at the edge of the funnel.
​

Question 49

How many 1-cent stamps are there in a dozen?
​
__________ stamps
​

Question 50

If you take 5 cards from a deck of 65 cards, how many cards do you have? ​

A) 52 cards
B) 5 cards
C) 60 cards
D) 70 cards
E) 13 cards

Question 51

If you take 7 cards from a deck of 52 cards, how many cards do you have?
​
__________ cards
​

Question 52

Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground (see figure below). It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1,006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, "If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the rope's length by a foot. Is it possible to reach the central ankh tower and touch it? ​ ​
Ahmes' dilemma. Note that there are two ankhshaped towers. One stands on a cylindrical platform in the center of the funnel. The platform's surface is at ground level. The distance from the platform surface to the liquid is 500 ft. The other ankh tower is on land, at the edge of the funnel.
​

A) Yes
B) No

Question 53

There are 5 separate, equal-size boxes, and inside each box there are 4 separate small boxes, and inside each of the small boxes there are 3 even smaller boxes. How many boxes are there all together? ​

A) 85 boxes
B) 80 boxes
C) 65 boxes
D) 90 boxes
E) 60 boxes