MedEntry

Trusted UCAT prep.

UMAT test tactics and preparation part 7: worded mathematical problems

Worded mathematical problems on the UMAT exam: translating worded problems into mathematical symbols.

comprehenisve UMAT advice from the team at MedEntry UMAT preparation.

Possibly the most confusing questions on the UMAT exam, worded mathematical problems can actually be solved relatively easily if you understand how the question is written and what the words of the question really mean in mathematical terms.

Prior to solving worded mathematical problems on the UMAT exam, it is essential that you are comfortable with translating words into mathematical symbols. Below is a partial list of words and their mathematical equivalents. You should know these by heart before attempting any of the worded mathematical problems as present in the UMAT exam.

 

Concept

Symbol

Words

Example

Translation

equality

=

is

2 plus 2 is 4

2 + 2 = 4

equals

x minus 5 equals 2

x-5 = 2

is the same as

multiplying x by 2 is the same as dividing x by 7

2x = x/7

addition

+

sum

the sum of y and pi is 20

y + pi = 20

plus

x plus y equals 5

x + y = 5

add

how many marbles must John add to collection P so that he has 13 marbles

x + P=13

increase

a number is increased by 10%

x + 10%x

more

the perimeter of the square is 3 more than the area

P = 3+A

subtraction

-

minus

x minus y

x-y

difference

the difference of x and y is 8

lx-yl = 8

subtracted

x subtracted from y

y-x

less than

the circumference is 5 less than the area

C = A-5

multiplication

x or * or .

times

the acceleration is 5 times the velocity

a = 5v

product

the product of two consecutive integers

x(x+ 1)

of

x is 125% of y

x = 125%y

division

/

quotient

the quotient of x and y is 9

x/y = 9

divided

if x is divided by y, the result is 4

x / y = 4

 

Worded mathematical problems on the UMAT exam: tips on how to go about your ‘translation’.

Although exact steps for solving worded mathematical problems on the UMAT exam cannot be given, the following guidelines will help:

  1. Firstly, choose a variable to stand for the least unknown quantity, and then try to write the other unknown quantities in terms of that variable. For example, suppose that Sue’s age is 5 years less than twice Jane’s age and the sum of their ages is 16. Then Jane’s age would be the least unknown, and we let x = Jane’s age. Expressing Sue’s age in terms of x gives Sue’s age = 2x – 5.
  2. Secondly, write an equation that involves the expressions in Step 1. Most (though not all) worded mathematical problems pivot on the fact that two quantities in the problem are equal. Deciding which two quantities should be set as equal is usually the hardest part in solving a worded mathematical problem. For the example above, we would get (2x – 5) + x = 16.
  3. Finally, solve the equation in Step 2 and interpret the result.

 

From the example above, we would get by adding the x’s: 3x-5 = 16
Then adding 5 to both sides gives 3x =21
Finally, dividing by 3 gives x = 7
Hence, Jane is 7 years old and Sue is 2x – 5 = 2 * 7 – 5 = 9 years old.

 

Worded mathematical problems on the UMAT exam: typical UMAT question types and what to look out for when solving them.

Motion problems

Virtually all motion problems involve the formula Distance = Rate * Time, or

 D=R * T

  • Overtake: In this type of problem, one person catches up with or overtakes another person. The key to these problems is that at the moment one person overtakes the other they have traveled the same distance.
  • Opposite Directions:  In this type of problem, two people start at the same point and travel in opposite directions. The key to these problems is that the total distance traveled is the sum of the individual distances traveled.
  • Round Trip: The key to these problems is that the distance going to the destination is the same as the distance returning from a destination.
  • Compass Headings:  In this type of problem, typically two people are travelling in perpendicular directions. The key to these problems is often the Pythagorean Theorem.
  • Circular Motion: In this type of problem, the key is often the arc length formula S = R?, where S is the arc length (or distance traveled), R is the radius of the circle, and ? is the angle.

Work problems

The formula for work problems is Work = Rate * Time, or W = R * T.   The amount of work done is usually 1 unit. Hence, the formula becomes 1 = R * T.

Solving this for R gives R = 1/T

Mixture problems

The key to these problems is that the combined total of the concentrations in the two parts must be the same as the whole mixture.

Coin problems

The key to these problems is to keep the quantity of coins distinct from the value of the coins.

Age problems

Typically, in these problems, we start by letting x be a person’s current age and then the person’s age a years ago will be x – a, and the person’s age a years in the future will be x + a.

Interest problems

These problems are based on the formula:

INTEREST = AMOUNT * TIME * RATE

Often, the key to these problems is that the interest earned from one account plus the interest earned from another account equals the total interest earned:

Total Interest = (Interest from first account) + (Interest from second account) 

 

For more helpful UMAT tips and UMAT advice please see MedEntry UMAT preparation and keep following our  weekly blog updates on UMAT test tactics and preparation

UMAT test tactics and preparation part 8: practica...
A comparison of medicine at Usyd and UNSW
Ethical Dilemma Questions UCAT Exam Psychometric tests UCAT Preparation UCAT Test Tips HPAT Preparation UCAT advice UMAT anxiety mmi sample answer UCAT Test Date LMS Update UMAT Skills UCAT Stress ACER Studying Medicine Medicine at Melbourne UMAT compared to school Medicine Counting Problems UCAT Test Medical Interview UMAT Results Time Management UCAT 2019 UCAT Training UCAT Scores mmi sample question UCAT UCAT Abstract Reasoning UCAT Study UMAT Coaching Sydney UMAT resources Process of Elimination UMAT Courses New Zealand UCAT workshop Sample Interview Questions UMAT Practice University Entrance Applications USyd Multistation Mini Interviews UCAT Situational Judgement Test Medical Entrance Interview Questions Pearson VUE English 2019 UCAT Registrations Situational Judgement Test UMAT Practice questions University fees UMAT Test tactics Video Blog UMAT Coaching GAMSAT UCAT Booking UMAT Section 1 Logical Reasoning & Problem Solving UMAT Test Tips UCAT App Medicine at Monash Percentage questions UMAT Exam UMAT Problems UMAT Courses Toowoomba UMAT Courses Darwin UCAT exam UMAT Preparation Courses Sample UMAT Questions Speed Reading in UMAT UMAT Training UMAT Section 3 Non Verbal Reasoning UMAT Tutoring UNSW UCAT Preparation Courses Year 12 Free UMAT questions UMAT Section 2 Understanding People UMAT Forums mmi ethical dilemma UCAT Coaching Resilience UMAT questions UMAT Queensland UMAT advice Interview UMAT Motivation UMAT Test Sample MMI UCAT Practice Discrimination Multiple Choice Study Tips Which Uni? UCAT Results mmi scoring UMAT Prep Careers Teachers HPAT UMAT Study Active learning Speed Reading in UCAT UCAT Prep UMAT scores University Rankings MedEntry LMS Update UCATSEN Probability UMAT tips UMAT vs ATAR UMAT Preparation UMAT Tuition UMAT Stress UMAT MMI UCAT Registration umat 2019 UCAT Practice Test UCAT Anxiety UMAT Courses UCAT Course UCAT Date UMAT Workshops Online UMAT Prep UCAT Tips

trhdtre tre



Get our new Free UCAT Practice Exam!