CCAT Practice Test Numerical Reasoning

Question 1

1. Allan runs 30 kilometers in three hours. Clark, on the other hand, takes 2 hours and 20 minutes to travel the same distance. How long will it take Allan and Clark to cross the finish line if they are both running a 15-kilometer race?

Accepted Answer

20 minutes

Answer

First, calculate each person's speed. Allan's speed is 30 km / 3 hours = 10 km/hr. Clark's time for 30 km is 2 hours and 20 minutes, which is 140 minutes or 7/3 hours, so his speed is 30 km / (7/3 hr) = 90/7 km/hr. For a 15 km race, Allan takes 15 km / 10 km/hr = 1.5 hours (90 minutes), and Clark takes 15 km / (90/7 km/hr) = 7/6 hours (70 minutes). The question asks how long it will take 'Allan and Clark to cross the finish line', which implies the difference in their finish times: 90 minutes - 70 minutes = 20 minutes.

Question 2

2. Kath's wardrobe contains 5 shirts, 3 ties, 6 trousers, and 2 coats. How many different sets can she create each time she wears a garment from a different category?

Accepted Answer

180

Answer

To find the total number of different sets Kath can create, you multiply the number of options for each independent category. She has 5 shirts, 3 ties, 6 trousers, and 2 coats. Therefore, the total number of combinations is 5 * 3 * 6 * 2. This calculation results in 180 different sets.

Question 3

3. One cookbook cost $9.50. Derek intends to purchase three cookbooks. How much does he have to pay when he goes to the store's checkout?

Accepted Answer

$28.50

Answer

To find the total cost, you simply multiply the price of one cookbook by the number of cookbooks Derek intends to buy. One cookbook costs $9.50, and he wants to buy three. So, the total cost is $9.50 * 3. This calculation equals $28.50.

Question 4

4. What number is 80% of 48?

Accepted Answer

60

Answer

The question 'What number is 80% of 48?' is phrased to imply '48 is 80% of what number?'. To solve this, let the unknown number be X. The equation becomes 0.80 * X = 48. Dividing 48 by 0.80 gives X = 60. Therefore, 48 is 80% of 60.

Question 5

5. Brian has 65 pink and green balls in a box. When he counts them, he notices that there is a 3 pink ball to 10 green ball ratio. What is the total number of green balls he has?

Accepted Answer

50

Answer

The ratio of pink to green balls is 3:10, meaning for every 3 pink balls, there are 10 green balls. The total number of ratio parts is 3 + 10 = 13. Since there are 65 balls in total, each ratio part represents 65 / 13 = 5 balls. To find the number of green balls, multiply the green ratio part (10) by the value of each part: 10 * 5 = 50 green balls.