TMUA Word Problems and Puzzles

TMUA likes to throw in word problems and puzzles on a variety of subjects. The best way to study for this is to do the past questions, because they can literally be on any topic under the sun (to name but a couple, finding the minimum number of attempts needed to guess a password and the various ways of arranging truth tellers and liars in a 3x3 grid).

For those so interested, we offer both one to one TMUA coaching on word problems and puzzles, as well as online group coaching via Zoom - 'TMUA Pattern Finding and Word Problems'  is Session #16 of 20' . Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our  'Online Coaching FAQ'.

Feel free to contact us if you require more information regarding any of the above.

Free Revision Resources

The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on word problems and puzzles - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.

• Teaser #42- tests understanding of degrees between clock hour and minute hand - Mild
• Teaser #30 - tests ability to calculate Bert's Age from a word problem - Mild
• Teaser #39 - tests ability to work out who won a tiddlywinks tournament - Mild
• Teaser #36 - tests ability to solve a swimming pool draining word problem - Mild
• Teaser #182 - tests knowledge of divisibility rules in a puzzle - Fairly Mild
• Teaser #119 - tests ability to count Andy's socks - Fairly Mild
• Teaser #375 - tests ability to calculate basic probabilities in a 'balls in bag' game - Standard
• Teaser #94 - tests understanding of percentage increases (calculation too hard for TMUA, method useful) - Standard
• Teaser #463 - tests how to find the number of terms in an arithmetic sequence given certain criteria - Standard
• Teaser #135 - tests ability to extract ratio and surface area of cuboid information to answer the word problem - Standard
• Teaser #52 - tests ability to solve a 'games night' puzzle - Standard
• Teaser #82 - tests understanding of probability that a result is a false positive - Standard
• Teaser #77 - tests how to recalculate mean once a competitor drops out - Standard
• Teaser #78 - tests ability to work out probabilities in a fairground game - Standard
• Teaser #95 - tests knowledge of how to split a pyramid in two by volume - Standard
• Teaser #97 - tests understanding of probability two balls picked are different colours given ratios of balls in bag - Standard
• Teaser #483 - tests ability to discover which of five options is the only possible first term of an arithmetic progression - Standard
• Teaser #133 - tests ability to solve a 'Work Word Problem' - Standard
• Teaser #99 - tests ability to apply Heron's Formula to a triangle word problem (the final calculation is beyond TMUA) - Standard
• Teaser #124 - tests ability to solve a 'Work Word Problem' - Standard
• Teaser #121 - tests how to find the radius of a reduced sphere - Standard
• Teaser #123 - tests how to solve a word problem involving products of numbers - Standard
• Teaser #70 - tests ability to calculate expected throws of one dice before two consecutive sixes - Standard
• Teaser #89 - tests distance, speed and time with a common trap - Standard
• Teaser #80 - tests finding expected rolls of a dice to complete a board game - Standard
• Teaser #109 - tests ability to find probability a girl sits between her friends - Standard
• Teaser #238 - tests ability to solve a board based maths coin placing counting puzzle - Medium
• Teaser #49 - tests ability to understand coin toss probabilities in a game - Medium
• Teaser #93 - tests finding expected score on a dartboard based on probability of landing in certain areas - Medium
• Teaser #83 - tests how to find a person's age given almost no information (uses primes factorisation) - Medium
• Teaser #51 - tests ability to manipulate percentages to solve a followers puzzle - Medium
• Teaser #62 - tests calculating probability of false positive at a Taylor Swift concert - Standard
• Teaser #73 - tests ability to solve a seemingly impossible word problem using prime factors - Medium
• Teaser #60 - tests ability to calculate probabilities in a simple dice game - Medium
• Teaser #68 - tests ability to extract equation from word problem and solve - Medium
• Teaser #81 - tests ability to extract information from a word problem and put on Venn Diagram and solve - Medium
• Teaser #106 - tests understanding of how to calculate compound interest (the final calculation is beyond TMUA) - Medium
• Teaser #48 - tests 'I think of a number' word problem - Medium
• Teaser #90 - tests understanding of compound interest calculations - (the calculation itself is beyond TMUA) - Medium
• Teaser #414 - tests manipulation of logs and then recognising coprime numbers - Medium
• Teaser #226 - tests counting expected number of cards turned over before second spade - Medium
• Teaser #145 - tests ability to solve a 'Work Word Problem' - Medium
• Teaser #399 - tests ability to extract relevant information from the problem given, and thus calculate a probability - Medium
• Teaser #370 - tests ability to extract relevant information from the problem given, and thus calculate a probability - Medium
• Teaser #331 - tests ability to enter relevant data into a Venn Diagram and work out a probability using basic combinatorics - Medium
• Teaser #499 - tests how to establish which of six statements is true, given that exactly one is - Quite Tough
• Teaser #485 - tests understanding of converse, inverse and contrapositive - Quite Tough
• Teaser #86 - tests ability to solve a crossword puzzle of sequences - Quite Tough

TMUA Past Questions on Word Problems and Puzzles: SP p2 q13; SP p2 q20; 2016 p1 q7; 2016 p2 q4; 2016 p2 q19; 2017 p2 q20; 2018 p1 q17; 2018 p2 q3; 2018 p2 q8; 2018 p2 q17; 2019 p2 q9; 2020 p2 q11; 2020 p2 q17; 2020 p2 q19

Practice makes perfect - good luck in your studies!