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Exam 1: The Nature of Problem Solving

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Question 21

Multiple Choice

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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

C) A) and B)
D) undefined

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Question 22

Multiple Choice

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

A)
B)
C)
D)
E) ​

F) C) and E)
G) None of the above

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Question 23

Multiple Choice

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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? ​

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

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? ​

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 ​

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

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

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

Perform the operations. ​ ​

Perform the operations. ​

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 __________ __________.

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

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 __________. ​

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

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.

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. ​

Find the seven pattern. ​

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

Perform the operations. ​ 6 + 8 × 5 ​