Problem Solving Flashcards

A store sells apples for $0.75 each and oranges for $1.25 each. If Maria spends exactly $10.00 buying a total of 10 pieces of fruit, how many apples did she buy?

Answer: 5

Let a = apples and o = oranges; a + o = 10 and 0.75a + 1.25o = 10, solving gives a = 5.

A rectangular garden has a perimeter of 48 m. If its length is twice its width, what is its area?

Answer: 128 m²

Width = 8 m, length = 16 m, area = 8 × 16 = 128 m².

Which strategy is most effective when a problem has many possible solutions and no obvious starting point?

Answer: Make an organized list of cases

Creating an organized list ensures all possibilities are examined without missing or repeating cases.

A clock shows 3:15. What is the angle between the hour and minute hands?

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°.

If the pattern 2, 6, 12, 20, 30 continues, what is the next term?

Answer: 42

Differences are 4, 6, 8, 10, 12 — the next term is 30 + 12 = 42.

A train travels from City A to City B at 60 km/h and returns at 40 km/h. What is its average speed for the entire trip?

Answer: 48 km/h

Average speed = 2(60)(40)/(60+40) = 4800/100 = 48 km/h using the harmonic mean formula.

A container holds 24 liters. You have a 5-liter jug and a 7-liter jug with no markings. How can you measure exactly 6 liters?

Answer: Fill the 7-liter, pour into 5-liter, leaving 2 liters — repeat three times

Filling the 7-liter and pouring off 5-liter three times gives 3×2 = 6 liters after combining two partial fills.