ISAT - International Student Admissions Mathematical Problem-Solving Questions and Answers — 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?
- 50 km/h
- 48 km/h (Correct answer)
- 52 km/h
- 45 km/h
Correct answer: 48 km/h
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?
- 1/9
- 2/21
- 1/12
- 1/11 (Correct answer)
Correct answer: 1/11
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?
- A 4% decrease (Correct answer)
- A 4% increase
- No change
- A 1% decrease
Correct answer: A 4% decrease
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?
- π/2
- 4/Ï€
- π/4 (Correct answer)
- 2/Ï€
Correct answer: π/4
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?
- 1/3
- 3/4
- 1/4
- 1/2 (Correct answer)
Correct answer: 1/2
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.
Question 6: If 'n' is an odd integer, which of the following expressions must result in an even integer?
- n + 2
- 2n + 1
- n - 4
- 3n + 5 (Correct answer)
Correct answer: 3n + 5
An odd integer multiplied by an odd integer (3) results in an odd integer. An odd integer (3n) plus another odd integer (5) results in an even integer. Let's test the options with n=3: A) 3+2=5 (Odd); B) 2(3)+1=7 (Odd); C) 3-4=-1 (Odd); D) 3(3)+5=14 (Even). This holds true for all odd integers.
ISAT - International Student Admissions Mathematical Problem-Solving Questions and Answers
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?