GCAT Reasoning 5 — Questions and Answers
Question 1: All squares are rectangles. Shape X is not a rectangle. What can we conclude?
- Shape X is a square
- Shape X might be a square
- Shape X is not a square (Correct answer)
- Shape X is a circle
Correct answer: Shape X is not a square
Using contrapositive: if not a rectangle, then not a square.
Question 2: A car depreciates 15% per year. If it costs $20,000 new, what is its value after 2 years?
- $14,450 (Correct answer)
- $14,000
- $13,000
- $16,000
Correct answer: $14,450
$20,000 × 0.85 × 0.85 = $20,000 × 0.7225 = $14,450.
Question 3: Find the missing number: 8 : 64 :: 5 : ___
- 25 (Correct answer)
- 10
- 50
- 15
Correct answer: 25
8 squared is 64; similarly, 5 squared is 25.
Question 4: In a group of 50 people, 30 like tea and 20 like coffee. 10 like both. How many like neither?
- 0
- 5
- 10 (Correct answer)
- 15
Correct answer: 10
Using inclusion-exclusion: 30 + 20 − 10 = 40 like at least one; 50 − 40 = 10 like neither.
Question 5: Which of the following is an example of deductive reasoning?
- The sun rose every day this week, so it will rise tomorrow
- All mammals breathe air; whales are mammals; therefore whales breathe air (Correct answer)
- Most students pass this test, so you will probably pass
- It rained after I washed my car three times, so washing causes rain
Correct answer: All mammals breathe air; whales are mammals; therefore whales breathe air
Deductive reasoning draws a guaranteed conclusion from universal premises applied to a specific case.
Question 6: Mirror image: The word 'MAPS' is reflected horizontally. What does it look like?
- SPAM (Correct answer)
- SPAM
- SDAM
- SQAM
Correct answer: SPAM
A horizontal reflection of 'MAPS' reverses the letter order to 'SPAM'.
Question 7: A project takes 12 days with 8 people. If 4 people leave after 6 days, how many more days are needed?
- 6
- 8
- 10 (Correct answer)
- 12
Correct answer: 10
Total work = 96 person-days; 6 days × 8 people = 48 done; remaining 48 ÷ 4 people = 12 more days.
GCAT Reasoning 5
All squares are rectangles.
Shape X is not a rectangle.
What can we conclude?