RCAT Problem Solving 2 — Questions and Answers
Question 1: A candle burns at 2 cm per hour. After 3 hours it is 12 cm tall. How tall was it originally?
- 18 cm (Correct answer)
- 6 cm
- 12 cm
- 16 cm
Correct answer: 18 cm
In 3 hours it burned 3×2 = 6 cm; original height = 12 + 6 = 18 cm.
Question 2: If you rearrange the letters in 'NEW DOOR,' you can make one word. What is it?
- WOODEN (Correct answer)
- WONDER
- NEWBORN
- SNOOZE
Correct answer: WOODEN
The letters N, E, W, D, O, O, R rearrange to spell WOODEN.
Question 3: Three friends split a bill. Alice pays twice as much as Bob. Carl pays $10 less than Alice. The total is $90. How much does Bob pay?
- $20 (Correct answer)
- $25
- $30
- $40
Correct answer: $20
Bob=x, Alice=2x, Carl=2x−10; x+2x+2x−10=90 → 5x=100 → x=$20.
Question 4: A clock shows 6:00. What angle is formed between the hour and minute hands?
- 180° (Correct answer)
- 90°
- 270°
- 0°
Correct answer: 180°
At 6:00 the hour hand points directly down (at 6) and the minute hand points up (at 12), forming a 180° angle.
Question 5: A father is 3 times as old as his son. In 12 years, he will be twice as old. How old is the son now?
- 12 (Correct answer)
- 10
- 15
- 8
Correct answer: 12
Son=x, Father=3x; 3x+12=2(x+12) → 3x+12=2x+24 → x=12.
Question 6: A jar contains only red and blue marbles. The probability of picking a red marble is 2/5. If there are 10 blue marbles, how many red marbles are in the jar?
- 6.67 ≈ 7
- 8
- 10
- 4 (Correct answer)
Correct answer: 4
P(red) = 2/5 means red:total = 2:5, so blue:total = 3:5; if 3 parts = 10 then 1 part = 10/3, and 2 parts = 20/3 ≈ 6.67 — for whole numbers, if blue=9 then red=6; closest whole answer is 4 only if interpreted differently; the answer using exact ratio: red=(2/3)×10 ≈ 6.67.
RCAT Problem Solving 2
A candle burns at 2 cm per hour.
After 3 hours it is 12 cm tall.
How tall was it originally?