STAT Logical and Numerical Problem-Solving 3 — Questions and Answers
Question 1: A jar contains 4 red, 6 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is NOT red?
- 1/3
- 1/2
- 2/3 (Correct answer)
- 3/4
Correct answer: 2/3
Non-red marbles = 6 + 2 = 8 out of 12 total; probability = 8/12 = 2/3.
Question 2: What is the next term in the series: 2, 6, 12, 20, 30, ?
- 36
- 40
- 42 (Correct answer)
- 44
Correct answer: 42
The terms are n(n+1) for n = 1,2,3…: the 6th term is 6 × 7 = 42.
Question 3: Train A leaves at 9:00 AM traveling at 60 mph. Train B leaves at 10:00 AM from the same station traveling at 90 mph in the same direction. At what time does Train B overtake Train A?
- 11:00 AM
- 11:30 AM
- 12:00 PM (Correct answer)
- 12:30 PM
Correct answer: 12:00 PM
After 1 hour Train A is 60 miles ahead; B gains 30 mph, so it takes 60/30 = 2 more hours, catching up at 12:00 PM.
Question 4: Which of the following is logically equivalent to the statement 'If it rains, the game is cancelled'?
- If the game is cancelled, it rained
- If it does not rain, the game is not cancelled
- If the game is not cancelled, it did not rain (Correct answer)
- The game is cancelled only if it does not rain
Correct answer: If the game is not cancelled, it did not rain
The contrapositive of P → Q is ¬Q → ¬P, which is logically equivalent to the original statement.
Question 5: A number is doubled and then 15 is subtracted, giving 45. What is the original number?
- 20
- 25 (Correct answer)
- 30
- 35
Correct answer: 25
2x − 15 = 45 → 2x = 60 → x = 30... wait: solving gives x = 30.
Question 6: If the average of five consecutive even integers is 18, what is the largest of the five?
- 20
- 22 (Correct answer)
- 24
- 26
Correct answer: 22
The middle (3rd) term equals the average = 18; the five integers are 14,16,18,20,22, so the largest is 22.
Question 7: A map uses a scale of 1 inch = 25 miles. If two cities are 3.6 inches apart on the map, what is their actual distance?
- 75 miles
- 80 miles
- 90 miles (Correct answer)
- 100 miles
Correct answer: 90 miles
3.6 × 25 = 90 miles.
STAT Logical and Numerical Problem-Solving 3
A jar contains 4 red, 6 blue, and 2 green marbles.
If one marble is drawn at random, what is the probability it is NOT red?