ISAT - International Student Admissions Mathematical Problem-Solving Questions and Answers

Question 1

A car travels from Town A to Town B at an average speed of 60 km/h and returns from Town B to Town A along the same route at an average speed of 40 km/h. What is the average speed for the entire round trip?

Accepted Answer

48 km/h

Answer

Average speed is calculated as Total Distance / Total Time. Let the distance between Town A and Town B be D. The time taken for the first leg is D/60 hours, and the time for the return leg is D/40 hours. The total distance is 2D. The total time is (D/60) + (D/40) = (2D + 3D) / 120 = 5D/120 = D/24. Therefore, the average speed is (2D) / (D/24) = 2D * (24/D) = 48 km/h.

Question 2

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?

Accepted Answer

1/11

Answer

There are a total of 5 + 4 + 3 = 12 marbles. The probability of the first marble being blue is 4/12. After drawing one blue marble, there are 11 marbles left, with 3 of them being blue. The probability of the second marble being blue is 3/11. The probability of both events happening is (4/12) * (3/11) = 12/132, which simplifies to 1/11.

Question 3

A stock's price increases by 20% in January and then decreases by 20% in February. What is the net percentage change in the stock's price from the beginning of January to the end of February?

Accepted Answer

A 4% decrease

Answer

Let the original price be P. After a 20% increase, the price becomes P * (1 + 0.20) = 1.2P. Then, this new price decreases by 20%, so the final price is (1.2P) * (1 - 0.20) = 1.2P * 0.8 = 0.96P. The final price is 96% of the original price, which represents a 4% decrease.

Question 4

A circle is inscribed perfectly within a square. What is the ratio of the area of the circle to the area of the square?

Accepted Answer

π/4

Answer

Let the side length of the square be 's'. The area of the square is s^2. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square, so d = s. The radius of the circle is r = d/2 = s/2. The area of the circle is πr^2 = π(s/2)^2 = πs^2/4. The ratio of the circle's area to the square's area is (πs^2/4) / s^2 = π/4.

Question 5

A painter can paint a house in 6 days, and their apprentice can paint the same house in 12 days. If they work together for 2 days, what fraction of the house remains unpainted?

Accepted Answer

1/2

Answer

The painter's work rate is 1/6 of the house per day. The apprentice's work rate is 1/12 of the house per day. Their combined rate is (1/6) + (1/12) = (2/12) + (1/12) = 3/12 = 1/4 of the house per day. In 2 days, they complete 2 * (1/4) = 1/2 of the house. Therefore, the fraction of the house that remains unpainted is 1 - 1/2 = 1/2.

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Mathematical Problem-Solving Questions and Answers