Free MSAP Reasoning in the Sciences and Mathematics Questions and Answers

Question 1

In the grid below, the letters represent different whole numbers of less than 20. The numbers to the right and below the grid are row and column totals.  The value of Q is:

Accepted Answer

9

Answer

Explanation:
The value of Q is 9.

Question 2

Which one of the schedules meets the requirements of the Firefighters’ Union?

Accepted Answer

II

Answer

Explanation:
The schedules that meet the requirements of the Firefighters’ Union is column II.

Question 3

A schedule can be thought of as a set of v objects (in this case, firefighters) that have to be arranged into b sets (in this case, one set for each day of the week) all of size k and such that each object occurs the same number of times (r) in the schedule and only once in any set. For the firefighters’ schedules, v = 7, b = 7, k = 3, and r = 3.

If v = 3, b = 6, k = 1, r = 2, which one of the following completes the schedule {1}, {2}, {3}, {1}, {2}, . . .?

Accepted Answer

{3}

Answer

Explanation:
Given that each set in the schedule should contain only one firefighter (as k = 1), and the requirement that each object occurs the same number of times in the schedule (r = 2), the firefighter that has not yet appeared in the schedule is 3. Therefore, adding Firefighter 3 to the next position completes the schedule correctly.

Question 4

The schedule {1,2}, {2,3}, {x,y} is a schedule for which v = 3, b = 3, k = 2, r = 2, if:

Accepted Answer

x = 1, y = 3

Answer

Explanation:
For the schedule to meet the conditions where each set contains two firefighters (k = 2) and each firefighter appears twice in the schedule (r = 2), the values of x and y must be chosen such that all firefighters are included twice. Since firefighters 1, 2, and 3 are involved, setting x = 1 and y = 3 ensures that all three firefighters are included twice, meeting the requirements.

Question 5

In a class of 25 students, 16 students are proficient in mathematics and 18 students are proficient in science. How many students are proficient in both mathematics and science?

Accepted Answer

9

Answer

Explanation:
This can be found by adding the number of students proficient in mathematics (16) and the number of students proficient in science (18), then subtracting the total number of students (25) to find the overlap.

MSAP - Mature Students Admissions Pathway Practice Test

MSAP - Mature Students Admissions Pathway Practice Test

Free MSAP Reasoning in the Sciences and Mathematics Questions and Answers