# UMAT SAMPLE Questions

## Construct 1 - Logical Reasoning and Problem Solving

Question 1

The following table shows the number and rate of deaths due to transport accidents and assaults for young Australians.

With respect to young Australians in 2004, which of the following can be best concluded from the table above?

A. A transport accident is a more common occurrence than an assault.

B. About 25% of the persons aged 18-24 dying from a transport accident were female.

C. 0.093% of females aged 18-24 died as a result of a transport accident.

D. Transport accidents and assaults are a major cause of death amongst the young Australian cohort.

Explanation: A is incorrect because although the number of deaths may be higher due to transport accidents, this does not imply that transport accidents occur more often (instead, assaults may occur more often but only lead to minor injuries, not death). C is incorrect because if 9.3 females die per 100,000 young females, then the percentage is 0.0093% (9.3/100000 = 0.000093 = 0.0093%). D is incorrect because this table does not make any comparison of transport accidents/assaults to other causes of death amongst young people, so it is impossible to conclude how major a cause these are. B is correct because there are 88 females in the 340 people aged 18-24 who died in a transport accident, which is equivalent to roughly 25%.

Source: Young Australians: their health and wellbeing 2007 Australian Institute of Health and Welfare Canberra

Questions 2-5

This unit describes a process for creating a number sequence.

A Szabo sequence is created by finding the sum of the digits of a whole number, then adding this sum to the whole number to get the next term in the sequence.

For example, the next term after 403 is 410, since 403 + (4 + 0 + 3) = 410.

By repeating this process, we get successive terms of the sequence:

403, 410, 415, 425, 436, 449 ...

In this sequence, 410 is referred to as the term immediately prior to 415.

Any whole number can be used as the first term, or seed number, of a Szabo sequence. The seed number of the standard Szabo sequence is 1:

1, 2, 4, 8, 16, 23, 28, 38, 49, 62...

Question 2

Each of the numbers from 91 to 95 inclusive is used as the seed number of five different Szabo sequences.

The three seed numbers which produce sequences that have 107 as a member are

(A)     91, 92 and 94.

(B)     91, 94 and 95.

(C)     91, 92 and 95.

(D)     92, 94 and 95.

The correct answer is A

91: 101, 103, 107

92: 103, 107

94: 107

95: 109

Question 3

What is the sum of the digits of the term immediately prior to 704 in a Szabo sequence?

(A)     11

(B)     15

(C)     18

(D)     19

The correct answer is D

We are looking for what number is added to the previous number to get 704. Subtract the answer choice from 704 then add up the digits, if the answer given is the same as the answer choice then it is correct.

(A) is incorrect as this would put the previous number as 693 which adds up to 18 instead of 11.

(B) is incorrect as this would put the previous number as 689 which adds up to 23 instead of 15.

(C) is incorrect as this would put the previous number as 686 which adds up to 20 instead of 18.

(D) is correct as this would put the previous number as 685 which adds up to 19.

The following additional information refers to questions 4-5.

Some numbers only appear in Szabo sequences if they are the seed number, because no number can immediately precede them.

For example, we can prove that 53 has no term immediately prior to it.

A search for it starts in the low fifties, but because 50 — the smallest number in the fifties — is followed by 55, we won't be able to reach 53 from 50 or any larger number.

From the forties we find that 44 immediately precedes 52, that 45 immediately precedes 54, but that 53 misses out.

The largest number in the thirties, 39, is followed by only 51. No smaller number needs to be tried.

Therefore 53 has no term immediately prior to it, which means that 53 can appear in a Szabo sequence only as the seed number.

Also, there are numbers which have two different terms immediately prior to them.

For example, 505 can be reached from 500 and 491. This is called merging.

Any number which is not a multiple of three produces a Szabo sequence which eventually merges with the standard Szabo sequence.

Question 4

The Szabo sequence which has 64 as its seed number merges with the standard Szabo sequence at

(A)     115.

(B)     122.

(C)     127.

(D)     128.

The correct answer is A

Question 5

A merge graph shows the standard Szabo sequence in rectangles and other sequences in circles.

Which of these merge graphs correctly shows how a sequence containing 178 and another sequence containing 187 merge with the standard Szabo sequence?

The correct answer is B

178: 194, 208, 218

187: 203, 208, 218

The two sequences merge at 208, (eliminate C) and both sequence have a single step between the seed number and the merging so the answer is B.

Question 6

Computer Scientist: It is inevitable that a computer program will eventually be able to defeat a human opponent at chess every time they play. Current computers can plot out millions of move permutations every second, and future computers will have even greater computational power. Humans, unable to match the computers' computational abilities, will not be able to prevail in a single match.

Chess Player: Your conclusion is incorrect. "While computers may possess vast computational abilities, they lack the capacity for insight and innovation demonstrated by all great chess players.

Which of the following can be best inferred from the statements of the chess player above?

A.   A computer with a capacity for insight and innovation could defeat any human player.

B.   Computers may defeat all human chess players consistently, but they are unable to enjoy either the game or the victory.

C.   Even the best computer chess programs are limited by the abilities of their programmers.

D.   Computational power alone is not sufficient to win consistently at the game of chess.

The correct answer is D

The chess player states that the scientist's conclusion — that a computer program will be able to consistently defeat human players because of its superior computational ability — is incorrect, and then he states that computers do not have the capacity for insight and innovation. The clear implication is that insight and innovation are necessary in order to be great at chess, and therefore it follows that computational ability alone is not sufficient. There is insufficient support for any of the other statements: Option A is unsupported because it is not specified whether this computer would have the computational power of other computers; option B contradicts the chess player’s statements as the chess player suggests that computers won’t beat great human chess players consistently; Option C is incorrect because the programmers are never discussed.

## Construct 2- Understanding People

Questions 1-3

Rob invited his parents for a weekend to visit him and his new fiancee, Helen, as well as to meet her parents. Helen insisted on cooking a meal for them all, however after a few hours waiting, it became clear they were not coming and Helen's parents departed. Having just rang his parents, Rob returns downstairs to the kitchen.

Rob: You're not going to throw that away are you? Be a shame if it went to waste.

Helen: Dunno, I could probably use it in a stir-fry or something.

Rob: Good. Hey, come on Helen – worse things have happened. Let’s clear everything away and flop down on the sofa with a bottle of wine. God knows, we've got enough of it.

Helen: You're really going to pretend nothing's happened? Don't you think we should talk about this? You haven't even told me what they said on the phone.

Rob: How am I pretending? I just don't want to dwell on it. You can see what my parents are really like now and how we're clearly better off without them in our lives.

Helen: People don't just not turn up Rob...That's really odd. Were they ever even coming? I didn't invite them, I don't know what they said on the phone! I thought you had started to patch things up?

Rob: Look, Helen, I booked a hotel room...of course I thought they were coming. Did you think I didn't? Maybe you think I didn't even invite them? That I let you drag your Mom and Dad over here all so I could make a complete fool of myself

Helen: No, no, of course not...I'm just trying to understand. Did something happen?

Rob: It really doesn't concern you Helen.

Helen: Of course it concerns me, they're going to be my family too soon! Rob – don't walk away!

Rob: Alright look, it was my Dad ok?  He's the one who refused to come and Mom being Mom just kow-towed to him. He's a bully Helen, that's all he is. And if he can't have things his own way...why do you think I moved to Canada?

Helen: I don't know. I thought.

Rob: I could have stayed on the farm, he wanted me to, but I knew I'd never be good enough!  I captained my Rugby team, I did the subjects he wanted, I got married far too young just to please him.

Helen: But what about your Mum? Surely she can stand up to him?

Rob: No no no, she's just as bad. Used to think she wasn't, but she is. I used to think that all the hen-pecking had just worn her down, but that was just an excuse. That's why I wasn't on the phone for very long just now. Informed me she wasn't allowed to speak to me, because he is still very disappointed in me. Well, if she didn't agree she could have gotten in the car and driven up here herself. The truth is, they are just nasty, bitter people.

Helen: Oh Rob...I'm sorry.

Rob: So there you are, that's my parents. Can you blame me for not wanting to inflict them on you?

Helen: It's alright Rob, you don't need to defend yourself to me. You have a new family now – me, Henry, my parents. If they don't like it, well, we can just manage without them!

Question 1.

Which of the following best describe the tone of Rob's comment 'God knows we've got enough of it'?

A. Critical and bitter

B. Wry and resigned

C. Facetious and irked

D. Pithy and amused

A is incorrect because at this juncture Rob does not seem particularly annoyed by his parents not showing up, unlike Helen. He regards the evening as a write-off and just wants to settle down on the sofa and 'clear everything away' and forget about it all.

B is correct because there is some humour in the comment, we learn from the introduction that it was at Helen's insistence that the dinner was held, and therefore the wine bought. We also later learn that Rob's difficulties with his parents are not new, as he moved to Canada to avoid his father it would appear. Therefore there is a sort of dry humour in remarking how much wine they have, and resigned also fits his preferred response of just relaxing and accepting that his parents had not arrived.

C is incorrect because while Helen may regard the statement as facetious, as she believes that Rob's parents not attending is far more serious than Rob does, Rob wouldn't see it as inappropriate. Irked is also incorrect because, as described, Rob is not annoyed at this point.

D is incorrect because while the comment is pithy, a suitable alternative to wry, amused is too strong to describe the tongue in cheek humour which Rob is expressing. He may be resigned about his parents not showing up, but to say he is amused is a step too far, as shown by the anger he later expresses.

Question 2.

Which of the following best describe how Helen would have said the comment 'No, no, of course not...I'm just trying to understand. Did something happen?'?

A. Defensively

B. Questioningly

C. Composedly

D. Mollifying

The repetition of 'No' in this comment shows that Helen is attempting to curb Rob's mounting anger, as shown also by how he is cut off in midsentence. A is incorrect because while the words may read as being defensive, within the context it is clear that this is not the best answer, because she doesn't just seek to defend her line of questioning, she also hopes to calm Rob down, she's 'just trying to understand', not suggesting that he didn't invite his parents or lied. B is incorrect, while there are questions in the comment, this adds very little to the description of the comment and does not capture the element of Helen calming Rob. C is incorrect because at this point in the argument she doesn't seem particularly composed, in fact she seems distinctly unnerved and rushes into Rob's diatribe to attempt to patch things up and clarify her concerns. D is correct because it describes trying to placate and sooth. This is very much a conciliatory move on Helen's part intended to downplay any criticism and ensure Rob knows that she is very much on his side.

Question 3.

Which of the following best describes Rob's attitude towards his mother?

A. Angered by her failure to assert her own point of view in a more forceful way

B. Disenchanted by continual disappointments he has endured at her hands

C. Betrayed by the realisation that she has failed to show up at such an important occasion, to meet his fiancee and future parents in law.

D. Disappointed at her not holding up their agreement without telling him in advance

Rob's attitude towards his mother is only specifically addressed in one of his comments, so this comment has to be read particularly carefully to differentiate between similar answers.

A is incorrect because it assumes that Rob's mother only acts pursuant to his father's wishes, that she is dominated by his will – and this is not in reality the case. Rob says he once thought that she was better than her father, but in reality she isn't – 'They' are nasty, bitter people – not he. She may say that she isn't allowed to talk to him because his father is 'very disappointed' in Rob, but from the rest of his comments it is appears that at least some of her actions are of her own will, and thus leading to the description ‘she’s just as bad’.

B is correct because disenchanted – driven to expect little and put off by continual disappointment – is a perfect description of Rob's disaffection with his mother. He used to think she wasn't so bad, but now doesn't make any excuses; she's 'just as bad'. Over time, his willingness to excuse her behaviour has seemingly eroded.

C is incorrect because it refers only to this occasion, whereas there appears to be a long history of Rob’s mother acting in a similar way. It does not seem as though he had much hope for the dinner, as it was at Helen's insistence, and he gets over the non-attendance of his parents quite quickly.

D is incorrect because it focuses too much on this one specific encounter, nothing in the text is mentioned about him wishing they had been told in advance, and disappointed is too weak a word to describe an event which culminates in him calling his parents 'Nasty bitter people'.

Questions 4-6

The following passage is from a recent novel.  It details a son as he prepares to tell his father some news.

Novel: The Street Sweeper by Elliot Perlman, 2011

"What's wrong?" William McCray asked his son. Charles was going to have to tell his father. He had no choice but to tell him but he decided to wait till he got him home and made him a drink. He was going to have to be quick on his feet and make something up to distract his father’s attention from the truth on the way home. He knew his father had had a nose for the truth all his life so it would be a mistake to say something too fanciful.  He had to think fast. But he was having trouble coping with his own distress. As they walked from the campus to the apartment everything seemed a little surreal. He waved to some colleagues in the distance. There were some students walking down the street in the same direction as Charles and his father. If they were to strike up a conversation with them it might distract his father for at least some of the way home. But then the students might want to talk to Charles about the very thing he was trying to keep from him till they got home. The students had just acknowledged him with a wave. They were catching up.

Question 4.

William McCray asks "What's wrong?"" in a _____ manner.

A) accusatory

B) suspicious

C) concerned

D) innocuous

No adverb is used in describing the question asked by William McCray which captures his neutral or rather innocuous tone. He asks the question in a simple and unthreatening way. Furthermore, there is little more description of William in the passage so therefore little evidence to suggest the manner in which he is asking the question. Therefore from what we can read in the passage, D is the correct answer. As a result, A, B and C are all incorrect because while they seem like possibilities in this sort of situation, nothing in the passage supports them in this particular case.

Question 5.

Charles is feeling

A) desperate

B) anxious

C) pressure from his father

D) distracted

Charles is described as being in a state of 'distress' which is further emphasised by the short and quick sentences which make up the passage and serve to reinforce his stressed state of mind. He is therefore anxious, making B the correct answer. While he is clearly experiencing feelings of anxiety, there is nothing to suggest that Charles is in such a state that he will resort to extreme measures to hide the truth. Rather the opposite is true for he is clearly planning on telling his father the truth (whatever that may be) so A is incorrect. C is also incorrect because his father's initial question "what's wrong?" presents itself in an unthreatening and rather more neutral sort of way which suggests no pressure from his father. D is also incorrect as the opposite is in fact true with Charles being fixated on what he is going to tell his father, rather than being distracted from it.

Question 6.

It is likely that what Charles is about to reveal to his father is

A) of importance

B) very personal

C) going to change his father's perception of him

D) insignificant

A is the correct answer because clearly Charles is concerned and 'distressed' about what he is about to reveal to his father; it is something of weight otherwise he would not be so anxious about it all. B is incorrect because there is nothing in the text to suggest that the information he is about to share is personal rather than professional. In fact, given that he is so worried about the presence of 'colleagues' and 'students' in the passage perhaps suggests that the information is of a more professional nature. C is again incorrect because it is a complete assumption that what Charles is going to tell his father will change his perception of him as while the passage makes it clear that the information is of importance, nothing suggests the former. And D is incorrect as well because Charles would be far less concerned and perhaps would not even be telling his father the information if it was insignificant.

## Construct 3 - Non-verbal Reasoning

Question 1

Select the picture that would most logically and simply be the next in the series

The dot on the top-right corner of the hexagon alternates between not moving and moving one corner anticlockwise. The dot on the bottom-left moves one spot anticlockwise the first turn, then two the next, this continues increasing by one each move. The arrow moves two and a half sides anticlockwise each time.

Question 2

Select the picture that would most logically and simply be the next in the series

Solution: In this series there are 3 components, a black circle, a vertical line and a horizontal line. The vertical line and horizontal line appear to form a cross when they overlap in the same box, however their movements remain separate throughout the series. The black circle moves diagonally to the bottom right and back up to the top left again when it reaches the bottom right hand corner. It alternates between moving 1 position and two positions. This means that in picture 5 the black circle must be located along that diagonal at the intersection of row 3 and column 3. The vertical line alternates between moving two spaces down and two spaces left. The horizontal line alternates between moving two spaces left and two spaces down. Both lines end up in row 2 of column 3 in picture 5, forming a cross. Therefore E is the correct answer as it is the option that satisfies this pattern.

Question 3

Select the segment that would most logically and simply complete the picture

In each row, the left and right squares are superimposed onto each other to make one image. Then this image is rotated 90 degrees clockwise to give the middle square.

Question 4

Select the segment that would most logically and simply complete the picture

The outer shape of column B is determined by the difference in sides between columns A and C. For example in the first row; the shape in A1 has 4 sides minus 1 for the circle in C1 meaning the shape in B1 must have 3 sides (triangle). Therefore in B2 there will be no outer shape as the difference between the number of sides of two triangles is 0. The middle circle alternates between black and white, therefore the middle circle will be white.

Question 5

The following figures can be arranged to form a logical sequence. Select the alternative (A, B, C, D or E) that most logically and simply fits in the middle of the sequence.

The sequence is displayed in the correct order (DABCE) below:

The number of sides of the black shape within the grid increases by 2 each move, from 6 to 8, 10, 12 and finally 14.

Question 6

The following figures can be arranged to form a logical sequence. Select the alternative (A, B, C, D or E) that most logically and simply fits in the middle of the sequence.

A                                B                               C                               D                               E