STAT Logical and Numerical Problem-Solving 4

Question 1

In a group of 50 students, 30 study French, 20 study German, and 8 study both. How many study neither language?

Accepted Answer

8

Answer

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)?

Accepted Answer

$14,400

Answer

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?

Accepted Answer

120

Answer

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)?

Accepted Answer

22

Answer

3x − 12 = 2x + 10 → x = 22.

Question 5

Look at the pattern: △○△○○△○○○△. How many circles follow the 5th triangle?

Accepted Answer

5

Answer

The pattern shows 0, 1, 2, 3, 4 circles after each successive triangle; after the 5th triangle there are 5 circles.

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