RCAT Problem Solving

Question 1

A farmer has 17 sheep. All but 9 die. How many are left?

Accepted Answer

9

Answer

'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?

Accepted 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

Answer

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?

Accepted Answer

5 days

Answer

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?

Accepted Answer

66

Answer

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?

Accepted Answer

$0.05

Answer

If ball = x, bat = x + $1.00; x + (x+1.00) = 1.10 → 2x = 0.10 → x = $0.05.

RCAT - Revelian Cognitive Ability Test Practice Test