Logical and Numerical Problem-Solving Flashcards

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

Answer: 8

Using inclusion-exclusion: 30 + 20 − 8 = 42 study at least one language; 50 − 42 = 8 study neither.

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)?

Answer: $14,400

20,000 × 0.85 × 0.85 = 20,000 × 0.7225 = $14,450 — closest answer is $14,450.

Six people sit in a row. Alice must sit immediately to the left of Bob. How many valid arrangements are there?

Answer: 120

Treat Alice-Bob as one unit; arrange 5 units in 5! = 120 ways.

What value of x satisfies: 3(x − 4) = 2(x + 5)?

Answer: 22

3x − 12 = 2x + 10 → x = 22.

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

Answer: 5

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

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?

Answer: 3 hours

Combined rate = 1/4 + 1/6 − 1/12 = 3/12 + 2/12 − 1/12 = 4/12 = 1/3; time = 3 hours.

A statement reads: 'Some A are B; all B are C.' Which conclusion is necessarily true?

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.