NBT Logical Reasoning & Problem Solving 3 — Questions and Answers
Question 1: In a logical argument, if the premise "If it rains, the match is cancelled" is true, and "the match was not cancelled," what can be logically concluded?
- It definitely rained
- It did not rain (Correct answer)
- The match was postponed
- Nothing can be concluded
Correct answer: It did not rain
This is the rule of "modus tollens": If P → Q, and ¬Q, then ¬P. If rain → cancellation, and the match was NOT cancelled, then it did NOT rain.
Question 2: A sequence: 1, 4, 9, 16, 25, ___. What is the next term?
- 30
- 34
- 36 (Correct answer)
- 49
Correct answer: 36
The sequence consists of perfect squares: 1², 2², 3², 4², 5². The next is 6² = 36.
Question 3: A problem states: "It takes 3 workers 4 days to complete a task. How many days will 6 workers take to complete the same task?"
- 1 day
- 2 days (Correct answer)
- 3 days
- 4 days
Correct answer: 2 days
Total work = 3 × 4 = 12 worker-days. With 6 workers: 12 ÷ 6 = 2 days.
Question 4: Which of the following is an example of inductive reasoning?
- All prime numbers greater than 2 are odd; 7 is prime; therefore 7 is odd.
- The sun has risen every day in recorded history; therefore it will rise tomorrow. (Correct answer)
- If temperatures drop below 0°C, water freezes; temperatures are below 0°C; so water is frozen.
- No prime numbers are even; 4 is even; therefore 4 is not prime.
Correct answer: The sun has risen every day in recorded history; therefore it will rise tomorrow.
Inductive reasoning draws general conclusions from specific observations. Observing that the sun has risen every day leads to the general conclusion it will keep rising — this is a probabilistic, not guaranteed, conclusion.
Question 5: Five people sit in a row. Amahle sits between Sipho and Zanele. Thandi sits at one end. Rethabile does not sit next to Thandi. Which of the following seating arrangements is possible?
- Thandi, Sipho, Amahle, Zanele, Rethabile (Correct answer)
- Rethabile, Thandi, Sipho, Amahle, Zanele
- Thandi, Rethabile, Sipho, Amahle, Zanele
- Rethabile, Sipho, Amahle, Zanele, Thandi
Correct answer: Thandi, Sipho, Amahle, Zanele, Rethabile
Check: Thandi at one end (position 1). Amahle is between Sipho and Zanele (positions 2,3,4 or 3,4,5). Rethabile not next to Thandi (not position 2). Option A: Thandi(1), Sipho(2), Amahle(3), Zanele(4), Rethabile(5). Amahle between Sipho and Zanele ✓. Rethabile at end (position 5), not next to Thandi ✓. Valid.
Question 6: A logical argument states: "Some students are athletes. All athletes are disciplined. Therefore some students are disciplined." Is this argument valid?
- No, because not all students are athletes
- Yes, it follows logically from the premises (Correct answer)
- No, because the conclusion is too strong
- Yes, but only if all students are athletes
Correct answer: Yes, it follows logically from the premises
The argument is valid. If some students are athletes, and all athletes are disciplined, then at least those student-athletes are disciplined — making "some students are disciplined" a logically valid conclusion.
NBT Logical Reasoning & Problem Solving 3
In a logical argument, if the premise "If it rains, the match is cancelled" is true, and "the match was not cancelled," what can be logically concluded?