Quantitative Problem Solving Assessment Question and Answers

Question 1

The 24 students in the class are 24 years old on average. When the age of the teacher is taken into account, the average rises by 1. What age is the teacher?

Accepted Answer

49 yr

Answer

The total age of 24 students with an average of 24 years is 24 * 24 = 576 years. When the teacher is included, there are 25 people, and the average age rises by 1 to 25 years. The new total age for 25 people is 25 * 25 = 625 years. Therefore, the teacher's age is the difference: 625 - 576 = 49 years.

Question 2

A decade ago, the father's age was three times that of his son. In ten years, the father will be twice as old as his son. What is the current age ratio between them?

Accepted Answer

4:1

Answer

Let F and S be the current ages of the father and son. From the first condition, F-10 = 3(S-10), which simplifies to F = 3S - 20. From the second condition, F+10 = 2(S+10), which simplifies to F = 2S + 10. Equating these expressions for F, we get 3S - 20 = 2S + 10, which solves to S = 30. Substituting S=30 into F = 2S + 10 gives F = 70. The current age ratio is 70:30, which simplifies to 7:3. (Note: The provided correct answer 4:1 is inconsistent with the problem statement as written.)

Question 3

Meena and Meera have a 4:3 age ratio, meaning that their combined ages equal 28 years. After eight years, the ratio of their ages will be?

Accepted Answer

6:5

Answer

Let Meena's age be 4x and Meera's age be 3x. Their combined age is 4x + 3x = 7x. Since their combined age is 28 years, 7x = 28, so x = 4. This means Meena is 4*4 = 16 years old and Meera is 3*4 = 12 years old. After eight years, Meena will be 16+8 = 24 and Meera will be 12+8 = 20. The new ratio of their ages will be 24:20, which simplifies to 6:5.

Question 4

What is the age of the youngest child if the five children were born three years apart and their total age is fifty years?

Accepted Answer

10 yr

Answer

Let the youngest child's age be x. Since the five children were born three years apart, their ages are x, x+3, x+6, x+9, and x+12. The sum of their ages is x + (x+3) + (x+6) + (x+9) + (x+12) = 5x + 30. Given that their total age is 50 years, we set 5x + 30 = 50. Solving for x, we get 5x = 20, which means x = 4. Therefore, the youngest child is 4 years old. (Note: The provided correct answer 10 yr is inconsistent with the problem statement as written.)

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Quantitative Problem Solving Assessment Question and Answers