PowerSchool Aptitude Test PowerSchool Aptitude Test: Puzzles 2 — Questions and Answers
Question 1: A clock shows 3:15. What is the angle between the hour and minute hands?
- 0°
- 7.5° (Correct answer)
- 52.5°
- 90°
Correct answer: 7.5°
At 3:15, the minute hand is at 90° and the hour hand is at 97.5° (3×30 + 15×0.5), giving a difference of 7.5°.
Question 2: In a group of 50 students, 30 play basketball, 25 play soccer, and 10 play both. How many play neither sport?
- 5 (Correct answer)
- 10
- 15
- 20
Correct answer: 5
Using inclusion-exclusion: 30 + 25 − 10 = 45 play at least one sport, so 50 − 45 = 5 play neither.
Question 3: What comes next in the series: 2, 6, 12, 20, 30, ?
- 40
- 42 (Correct answer)
- 44
- 48
Correct answer: 42
The differences are 4, 6, 8, 10, 12 — each difference increases by 2 — so the next term is 30 + 12 = 42.
Question 4: If all Bloops are Razzies, and all Razzies are Lazzies, which statement must be true?
- All Lazzies are Bloops
- All Bloops are Lazzies (Correct answer)
- No Bloops are Lazzies
- Some Razzies are not Lazzies
Correct answer: All Bloops are Lazzies
By transitivity: since Bloops ⊆ Razzies and Razzies ⊆ Lazzies, all Bloops must be Lazzies.
Question 5: A box contains 4 red, 5 blue, and 6 green balls. What is the minimum number of balls to draw (without looking) to guarantee at least 2 of the same color?
- 2
- 3
- 4 (Correct answer)
- 6
Correct answer: 4
With 3 colors, you could draw one of each (3 balls) and still have none matching, so you need 4 draws to guarantee a pair.
Question 6: A train 150 m long passes a pole in 15 seconds. How long will it take to pass a platform 300 m long?
- 30 seconds
- 35 seconds
- 40 seconds
- 45 seconds (Correct answer)
Correct answer: 45 seconds
Speed = 150/15 = 10 m/s; total distance = 150 + 300 = 450 m; time = 450/10 = 45 seconds.
Question 7: Which figure completes the pattern if shapes rotate 90° clockwise each step: ▲, ▶, ▼, ◀, ?
- ▲ (Correct answer)
- ▶
- ◀
- ▼
Correct answer: ▲
Each step rotates the triangle 90° clockwise, so after four rotations (◀ → ▲) the cycle repeats back to ▲.
PowerSchool Aptitude Test PowerSchool Aptitude Test: Puzzles 2
A clock shows 3:15.
What is the angle between the hour and minute hands?