STAT Logical and Numerical Problem-Solving 4 — Questions and Answers
Question 1: In a group of 50 students, 30 study French, 20 study German, and 8 study both. How many study neither language?
- 6
- 8 (Correct answer)
- 10
- 12
Correct answer: 8
Using inclusion-exclusion: 30 + 20 − 8 = 42 study at least one language; 50 − 42 = 8 study neither.
Question 2: A car depreciates by 15% each year. If it is worth $20,000 now, what will it be worth after 2 years (to the nearest dollar)?
- $14,400 (Correct answer)
- $14,450
- $14,450
- $14,405
Correct answer: $14,400
20,000 × 0.85 × 0.85 = 20,000 × 0.7225 = $14,450 — closest answer is $14,450.
Question 3: Six people sit in a row. Alice must sit immediately to the left of Bob. How many valid arrangements are there?
- 60
- 120 (Correct answer)
- 240
- 720
Correct answer: 120
Treat Alice-Bob as one unit; arrange 5 units in 5! = 120 ways.
Question 4: What value of x satisfies: 3(x − 4) = 2(x + 5)?
- 18
- 20
- 22 (Correct answer)
- 26
Correct answer: 22
3x − 12 = 2x + 10 → x = 22.
Question 5: Look at the pattern: △○△○○△○○○△. How many circles follow the 5th triangle?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
The pattern shows 0, 1, 2, 3, 4 circles after each successive triangle; after the 5th triangle there are 5 circles.
Question 6: A cistern has two inlet pipes that fill it in 4 hours and 6 hours respectively, and one outlet pipe that empties it in 12 hours. How long does it take to fill the cistern with all pipes open?
- 2 hours
- 3 hours (Correct answer)
- 4 hours
- 6 hours
Correct answer: 3 hours
Combined rate = 1/4 + 1/6 − 1/12 = 3/12 + 2/12 − 1/12 = 4/12 = 1/3; time = 3 hours.
Question 7: A statement reads: 'Some A are B; all B are C.' Which conclusion is necessarily true?
- All A are C
- No A are C
- Some A are C (Correct answer)
- All C are A
Correct answer: Some A are C
Since some A are B, and all B are C, those A that are B must also be C — so some A are C.
STAT Logical and Numerical Problem-Solving 4
In a group of 50 students, 30 study French, 20 study German, and 8 study both.
How many study neither language?