RCAT Problem Solving 1 — Questions and Answers
Question 1: A farmer has 17 sheep. All but 9 die. How many are left?
- 9 (Correct answer)
- 8
- 17
- 0
Correct answer: 9
'All but 9' means 9 survive; the phrase 'all but 9 die' means 9 sheep remain.
Question 2: You have a 3-liter jug and a 5-liter jug. How do you measure exactly 4 liters using only these two jugs and a water source?
- Fill 5L, pour into 3L, discard 3L, pour remaining 2L into 3L, fill 5L again, top up 3L (need 1L) leaving 4L in 5L (Correct answer)
- Fill 3L twice into 5L leaving 1L, discard, repeat
- Fill both and combine
- Cannot be done
Correct answer: Fill 5L, pour into 3L, discard 3L, pour remaining 2L into 3L, fill 5L again, top up 3L (need 1L) leaving 4L in 5L
Fill 5L → pour into 3L → 2L in 5L → empty 3L → pour 2L into 3L → fill 5L → pour 1L into 3L → 4L remains in 5L.
Question 3: A snail climbs 3 meters up a 10-meter wall each day but slides back 1 meter each night. How many days to reach the top?
- 4 days
- 5 days (Correct answer)
- 10 days
- 7 days
Correct answer: 5 days
Net gain = 2m/day; after 4 days the snail is at 8m; on day 5 it climbs 3m to 11m (reaches the top of 10m during day 5).
Question 4: There are 12 people in a room. Each person shakes hands with every other person exactly once. How many handshakes occur?
- 66 (Correct answer)
- 144
- 132
- 72
Correct answer: 66
Number of handshakes = C(12,2) = 12×11/2 = 66.
Question 5: A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
- $0.05 (Correct answer)
- $0.10
- $1.00
- $0.50
Correct answer: $0.05
If ball = x, bat = x + $1.00; x + (x+1.00) = 1.10 → 2x = 0.10 → x = $0.05.
Question 6: How many times does the digit '1' appear in numbers from 1 to 100?
- 21 (Correct answer)
- 20
- 11
- 19
Correct answer: 21
1,10,11(×2),12,13,14,15,16,17,18,19,21,31,41,51,61,71,81,91,100 = 21 occurrences of the digit '1'.
RCAT Problem Solving 1
A farmer has 17 sheep.
All but 9 die.
How many are left?