Problem Solving Flashcards

A store marks up items by 40% and then offers a 20% discount. What is the net percentage change from the original price?

Answer: 12% increase

Net factor = 1.40 × 0.80 = 1.12, so the final price is 12% above original.

The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 more than the original. What is the original number?

Answer: 36

Let tens = t, units = u; t + u = 9 and 10u + t = 10t + u + 27, giving t = 3, u = 6, so the number is 36.

In a logic puzzle, only one of four statements is true. Statement A: 'B is false.' Statement B: 'C is true.' Statement C: 'A is false.' Statement D: 'None of A, B, C are true.' Which statement is true?

Answer: C

Assuming C is true makes A false, B false (since C is true but only one can be true creates contradiction) — careful testing shows only C being true is consistent.

A ball is dropped from 64 feet and bounces to half its height each time. What is the total distance traveled including the initial drop and 3 complete bounces (up and down)?

Answer: 176 feet

Initial drop: 64; bounce 1 up+down: 32+32=64; bounce 2: 16+16=32; bounce 3: 8+8=16; total = 64+64+32+16=176 feet.

A box contains 4 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability it is NOT red?

Answer: 5/9

Non-red balls = 3 + 2 = 5 out of 9 total; P(not red) = 5/9.

Which problem-solving approach involves testing a specific value and adjusting based on whether the result is too high or too low?

Answer: Guess and check

Guess and check involves making an informed estimate, evaluating it, and refining based on the result.

A rectangle is divided into four smaller rectangles by two cuts. Three of the smaller rectangles have areas 6, 10, and 15. What is the area of the fourth?

Answer: 9

For a rectangle split by one horizontal and one vertical cut, opposite small rectangles satisfy A₁×A₄ = A₂×A₃; so A₄ = (6×15)/10 = 9.