AMCAT Math 2

Question 1

A train travels 360 km in 4 hours. If it increases its speed by 30 km/h, how long will it take to cover the same distance?

Accepted Answer

3 hours

Answer

Original speed = 360/4 = 90 km/h; new speed = 120 km/h; new time = 360/120 = 3 hours.

Question 2

If 2x + 3y = 12 and x - y = 1, what is the value of x?

Accepted Answer

3

Answer

From x - y = 1, x = y + 1; substituting into 2(y+1) + 3y = 12 gives 5y = 10, y = 2, x = 3.

Question 3

A rectangle has a perimeter of 54 cm and its length is twice its width. What is the area of the rectangle?

Accepted Answer

162 cm²

Answer

2(l + w) = 54 and l = 2w gives 2(2w + w) = 54, so w = 9, l = 18; area = 18 × 9 = 162 cm².

Question 4

What is the compound interest on $5,000 at 10% per annum for 2 years, compounded annually?

Accepted Answer

$1,050

Answer

CI = 5000(1.1)² - 5000 = 5000(1.21) - 5000 = 6050 - 5000 = $1,050.

Question 5

The average of 5 numbers is 20. If one number is removed, the average becomes 18. What is the removed number?

Accepted Answer

28

Answer

Sum of 5 numbers = 100; sum of remaining 4 = 72; removed number = 100 - 72 = 28.

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