Trusted UCAT prep.

UMAT test tactics and preparation part 5: Counting Problems in UMAT

Counting problems in UMAT: an essential summary.

Your UMAT questions explained by the team at MedEntry as part of our new section UMAT test tactics and preparation.

They may seem simple on paper, but counting problems contained within the UMAT exam can often cause much confusion among students. If you can understand the basic principles of counting problems and recognize when to apply them, you will be able to master many of the typical counting problem question types presented in the UMAT exam.


When counting elements that are in overlapping sets, the total number will equal the number in one group plus the number in the other group minus the number common to both groups. Venn diagrams are very helpful with these typical UMAT style problems.

Sample UMAT style question: If in a certain school 20 students are taking math and 10 are taking history and 7 are taking both, how many students are taking either math or history?


(A) 23

(B) 25

(C) 29

(D) 37


By the principle stated above, we add 10 and 20 and then subtract 7 from the result.
Thus, there are (10 + 20) – 7 = 23 students. The answer is (B).


The number of integers between two integers inclusive is one more than their difference.

Sample UMAT style questionHow many integers are there between 49 and 101, inclusive?


(A) 50

(B) 51

(C) 52

(D) 53


By the principle stated above, the number of integers between 49 and 101 inclusive is (101 – 49) + 1 = 53. The answer is (D). To make this clearer, choose smaller numbers, say, 9 and 11. The difference between 9 and 11 is 2. But there are three numbers between them inclusive—9, 10, and 11—one more than their difference.


Fundamental Principle of Counting: If an event occurs m times, and each of the m events is followed by a second event which occurs k times, then the first event follows the second event m * k times.

Sample UMAT style questionThe following diagram illustrates the fundamental principle of counting for an event that occurs 3 times with each occurrence being followed by a second event that occurs 2 times for a total of 3 * 2 = 6 events:



Sample UMAT style questionA drum contains 3 to 5 jars each of which contains 30 to 40 marbles. If 10 percent of the marbles are flawed, what is the greatest possible number of flawed marbles in the drum?


(A) 51

(B) 40

(C) 30

(D) 20


There are at most 5 jars each of which contains at most 40 marbles; so by the fundamental counting principle, there is at most 5 * 40 = 200 marbles in the drum. Since 10 percent of the marbles are flawed, there is at most 10% * 200 = 20 flawed marbles. The answer is (D).


For a more extensive data-base of UMAT questions and more detailed UMAT advice see MedEntry UMAT preparation.



UMAT test tactics and preparation part 6: statisti...
Melbourne vs. Monash Medicine: Should I study medi...
UMAT Test Tips mmi ethical dilemma UCAT Preparation Free UMAT questions UCAT Tips UCAT Prep UMAT Section 3 Non Verbal Reasoning LMS Update UMAT Study Medicine at Monash UCAT Stress Applications English Counting Problems mmi scoring Percentage questions UCAT Training HPAT Preparation Ethical Dilemma Questions UCAT Practice UMAT Prep Multistation Mini Interviews Pearson VUE UMAT Exam Medicine UCAT Booking UMAT tips Sample UMAT Questions UMAT Preparation Courses Which Uni? UMAT Problems UCAT Course UMAT Courses UCAT Results Resilience Medical Entrance UMAT Interview Questions GAMSAT Medicine at Melbourne UMAT Section 1 Logical Reasoning & Problem Solving University Entrance Psychometric tests UMAT Tuition UMAT compared to school Video Blog UCAT Study Studying Medicine Process of Elimination UCAT workshop Discrimination USyd UMAT Motivation UMAT advice UMAT Training Sample Interview Questions UCAT App UMAT Skills UMAT Courses New Zealand UMAT Tutoring Interview umat 2019 UCAT Date UCAT UCAT Coaching UMAT Test tactics ACER UCAT Situational Judgement Test mmi sample answer mmi sample question Active learning UCAT Exam UCAT Test Date MMI UMAT Courses Darwin UCAT Test Tips HPAT Year 12 Study Tips Sample MMI UMAT anxiety Situational Judgement Test UMAT Courses Toowoomba UCAT exam UMAT Practice UCAT Registration UMAT Queensland UMAT resources UMAT Workshops UNSW UMAT Results UCAT 2019 UCAT advice UMAT Practice questions Speed Reading in UCAT UMAT questions Multiple Choice UCATSEN UCAT Preparation Courses UCAT Scores UMAT Test UMAT Stress UMAT Preparation UMAT scores UCAT Test Medical Interview UMAT Coaching Sydney UMAT Forums UMAT vs ATAR UCAT Anxiety UCAT Abstract Reasoning Probability Careers Teachers 2019 UCAT Registrations University fees University Rankings UMAT Section 2 Understanding People Speed Reading in UMAT Time Management UCAT Practice Test MedEntry LMS Update Online UMAT Prep UMAT Coaching

trhdtre tre

Get our new Free UCAT Practice Exam!