GRADUATE MANAGEMENT ADMISSION TEST (GMAT) – QUANTITATIVE SECTION PRACTICE EXAMINATION 2026 |DEPARTMENT OF MATHEMATICS AND STATISTICS QUANTITATIVE REASONING PRACTICE EXAMINATION 2026 (Problem Solving & Data Sufficiency) SPRING SEMESTER EXAM 2026

GRADUATE MANAGEMENT ADMISSION TEST (GMAT) –
QUANTITATIVE SECTION PRACTICE EXAMINATION 2026
|DEPARTMENT OF MATHEMATICS AND STATISTICS
QUANTITATIVE REASONING PRACTICE EXAMINATION 2026
(Problem Solving & Data Sufficiency)

SPRING SEMESTER EXAM 2026



Combined Events

For events E and F:

• not E = P(not E) = 1 - P(E)

• E or F = P(E or F) = P(E) + P(F) - P(E and F)

• E and F = P(E and F) = P(E)P(F)




Multiplication Principle

The number of ways independent events can occur together can be determined by multiplying
together the number of possible outcomes for each event.




1st Rule of Probability: Likelihood of A

Basic rule: The probability of event A occurring is the number of outcomes that result in A
divided by the total number of possible outcomes.
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, 2nd Rule of Probability: Complementary events

Complementary Events: The probability of an event occurring plus the probability of the event
not occurring = 1.

P(E) = 1 - P(not E)




3rd Rule of Probability: Conditional Probability

Conditional Probability: The probability of event A AND event B occurring is the probability of
event A times the probability of event B, given that A has already occurred.

P(A and B) = P(A) × P(B|A)




4th Rule of Probability: Probability of A OR B

The probability of event A OR event B occurring is: the probability of event A occurring plus the
probability of event B occurring minus the probability of both

events occurring.

P(A or B) = P(A) + P(B) - P(A and B)




Probability of Multiple Events

Rules:

• A and B < A or B

• A or B > Individual probabilities of A, B

• P(A and B) = P(A) x P(B) ← "fewer options"

• P(A or B) = P(A) + P(B) ← "more options"
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, Indistinguishable Events (i.e., anagrams with repeating letters)

To find the number of distinct permutations of a set of items with indistinguishable ("repeat")
items, divide the factorial of the items in the set by the product of the factorials of the number
of indistinguishable elements.

Example: How many ways can the letters in TRUST be arranged? (5!)/(2!) = 60

5! is the factorial of items in the set, 2! is the factorial of the number of repeat items ("T"s)




Combinations (Order Does Not Matter)

nCr = n! / (r! (n - r)!)

Where n is the total number of items in the set and r is the number of chosen items.




Permutations (Order Does Matter)

nPr = n! / (n - r)!

Where n is the total number of items in the set and r is the number of chosen items.




Circular Permutations

The number of ways to arrange n distinct objects along a fixed circle is: (n - 1)!




Slope of a Line

y = mx + b
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m = slope = (difference in y coordinates)/(difference in x coordinates) = (y2 - y1)/(x2-x1)
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, 30-60-90 Triangle

30-60-90

x (shorter leg), x(sqrt 3) (longer leg), 2x (hypotenuse)




45-45-90 Triangle

45-45-90

x (shorter legs), x(sqrt 2) (hypotenuse)




Common Right Triangles

3-4-5 or 6-8-10 or 9-12-15

5-12-13




Number Added or Deleted

Use the mean to find number that was added or deleted.

• Total = mean x (number of terms)

• Number deleted = (original total) - (new total)

• Number added = (new total) - (original total)




Factors of Odd Numbers

Odd numbers have only odd factors
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