(1) The CIA wishes to send coded messages to its operatives in the field, and establish a secret
code to use with them.
If a letter is a vowel and comes before “M” in the alphabet, it will be encoded by writing down the
letter four letters before it (e.g. “E” is changed to “A”). If the letter is a consonant and comes
before “M” in the alphabet, it will be encoded by writing down the letter five letters before it. If the
letter is a vowel and comes after “P” in the alphabet, it will be encoded by writing down the letter
four letters after it. If the letter is a consonant and comes after “P” in the alphabet, it will be
encoded by writing down the letter five letters after it.
Which of these words is impossible to write using this code?
A)
EGG
B)
ILK
C)
CAB
D)
None, all are possible.
Answer: C
The code sounds complicated and long, but all that’s required of the candidate is simple
counting.
All letters come before the letter “M”, so half the code instructions are irrelevant. Overloading
a candidate with useless information is a common HPAT trick, and can make simple
questions seem overwhelming and complex.
Counting back four letters from each vowel and five from each consonant reveals that CAB
is the only word that’s impossible to write. This can be done at a glance, as all letters in CAB
are in the first three letters in the alphabet.
(2) The results of a survey amongst 1246 teenagers were used to determine the popularity of
different brands of chocolate sold in school canteens. The teenagers surveyed were from 8
different schools and were picked randomly from their classes. They were asked what biscuit
they’d last bought from the canteen, and when.
41% of students bought Chocolate Crunch.
23% of students bought Sugar Wisp.
21% of students bought Vanilla Delight.
8% of students bought Super Crunch.
5% of students bought Mega Choc.
2% of students bought Jiff Cakes.
50% of students bought their biscuit on the last day.
23% of students bought their biscuit yesterday.
21% of students bought their biscuit in the last week.
5% of students bought their biscuit in the last two weeks.
1% of students bought their biscuit in the last month.
What can be concluded from the above information?
I.
Jiff Cakes are the least popular biscuit nationwide
II.
If Mega Choc went off the market, Chocolate Crunch would become even
more popular
III.
If everyone who bought Vanilla Delight bought Sugar Wisp instead, it would
be the most popular biscuit.
A)
I and III
B)
II and III
C)
III
D)
I, II and III
Answer: C
Jiff cakes were the least popular biscuit surveyed; however the only people surveyed were
teenagers. This is not representative of all age groups, therefore it’s impossible to reach this
conclusion. Therefore we can eliminate (A) and (D), as they both include statement I.
While both biscuits have chocolate in their names, and would probably appeal to the same
consumers, it’s impossible to say which biscuits would receive the extra business if Mega
Choc went off the market. This allows us to eliminate option (B) and (D), as they both
include statement II.
Even without examining statement III, we can conclude that (C) is the correct answer, as
we’ve eliminated all other options. This is where you’d move on in the exam. However, for
completeness’ sake, a quick examination of the numbers reveals that 23 + 21 = 44, and 44
> 41. Therefore only statement III is correct, leaving (C) as the correct answer.
(2b)
What can be concluded from the above information?
I.
Every student who bought Sugar Wisp bought their biscuit yesterday.
II.
Students who bought their biscuit in the last two weeks were most likely to
purchase Mega Choc.
III.
Approximately half of students buy a biscuit every day.
A)
III
B)
II and I
C)
II
D)
None of the above
Answer: D
Statements I and II may seem true at first glance, as the statistics for Sugar Wisp and Mega
Choc seem to line up nicely with the statistics for “yesterday” and “in the last two weeks”.
However, it’s impossible to conclude with certainty.
Statement III is a little trickier, luring you in with “approximately”. However, the survey was
only taken at one time, and we don’t know when the survey was taken. For example, if the
survey was taken on a Friday, students could be more likely to treat themselves going into
the weekend, which would inflate the number of biscuits bought that day.
Therefore, none of the above statements are correct, leaving us with (D) as the correct
answer.
(3) The following graph pertains to deaths of officers in Dalamory Police Department over
the period of 2015, during the line of duty (i.e. deaths while away from the job are not
counted).
https://www.google.com/url?sa=i&url=https%3A%2F%2Ffox59.com%2Fnews%2Fpolice-fatality-report-car-accidents-among-top-cause-of-death%2Famp%2F&psig=AOvVaw0gjul9UhNoxgqPQiSa_RpT&u
st=1605958391022000&source=images&cd=vfe&ved=0CAIQjRxqFwoTCJilrq6Dke0CFQAAAAAdAAAAABAD
Based on the above graph, which of the following statements are incorrect?
1. “Domestic dispute” calls were the most common calls that the Dalamory Police
Department received that year.
2. Approximately one in forty-five deaths occurred during a dispatch call relating to a
house fire.
3. An officer is more likely to be injured during a “Disturbance” dispatch call than a
“Suspicious person/vehicle” call.
A) 1 and 3
B) 2 and 3
C) 2 only
D) 1, 2 and 3
Answer: A
The first thing a candidate should pay attention to here is the word “incorrect” in the question.
During the exam, this word should be underlined/circled/highlighted as it completely flips the
meaning of the question, so even a perfectly logical thought process can be derailed by missing
this. This is a common HPAT trick, so be wary!
1 is an incorrect statement as the graph only shows the proportion of officer deaths, rather than
how common a call type is overall. Therefore, we can eliminate (B) as an answer since it doesn’t
include 1, which we know must be part of the answer.
2 is a correct statement. 2% of 91 deaths would average to around one in 45 deaths. The word
“approximately” gives a little leeway here, as 2% of 91 is a close to 1 in 45 deaths, but not
exact. Therefore we can eliminate any answers that have statement 2.
This allows us to eliminate answer option (D). We’ve already eliminated (B) from the previous
statement, so there’s only (A) and (C) left.
Finally, we look at statement 3. This is incorrect, as the graph pertains only to deaths, not
injuries. While it could be assumed that incidents with higher death rates would also result in
more injuries, it is impossible to know for sure. Also, the candidate can ONLY work with what’s
presented to them here, and this rule stays concrete throughout all of the HPAT.
Therefore, statement 3 is incorrect, and must be included in the answer. This disallows (C), as it
doesn’t include statement 3. Therefore (A) is the correct answer.
(5) A racecourse is set up for a boat. The racecourse consists of four anchored marks, arranged
in a square with sides 2 km each. One mark is at the northwest corner, one at the southwest
corner, one at the northeast corner, and one at the southeast corner. The boat starts at the
southeast mark and heads directly north until it reaches a mark, where it makes a turn and
heads southwest. Upon reaching the southwest mark, it takes another turn and heads north.
Upon reaching the north mark, it takes a third turn, heading southeast from there. When it
reaches the southeast mark, the race finishes.
How far has the boat travelled after completing this course 1? Please select the option closest
to the answer.
A) 8 kilometres
B) 9.6 kilometres
C) 8.6 kilometres
D) 9 kilometres
Answer: B
For questions like this, don’t be afraid to draw a diagram! This seemingly complex route
becomes a very simple maths question once a diagram is present.
A candidate can draw all over the question booklet if they please, so this is an ideal space to
draw a quick diagram. It’s VERY important the candidate does not write ANYTHING on their
answer sheet except for marking each answer, as this will invalidate the exam.
As can be seen here, all the boat is doing is travelling two sides of a square, and two diagonals.
As previously stated, each side is 2km. Using some quick maths, you can work out that each
diagonal is about 2.82 kilometres. 2+2+2.82+2.82=9.64. This is closest to option (B), 9.6 km,
making it the correct answer.
(5b) Assuming a constant speed of 20 kilometres per hour, how long did it take the boat to
complete the course?
(A) 0.48 hours
(B) 0.45 hours
(C) 0.43 hours
(D) 0.3 hours
Answer: A
This question is simple, only requiring the candidate to divide their previous answer by 20 to find
the answer. The catch is, if the candidate was unable to answer the previous question, it’s
unlikely they’ll get this one correct.
However, this doesn’t mean a candidate unable to answer the previous question would have to
guess this one completely. Three of the answers ((A), (B) and (C)) match up to answers in the
previous question. However, option (D) does not. A resourceful candidate would attempt to
divide all options in question 5 by 20, and quickly realise that option (D) matches none of them,
making it obviously incorrect. This small amount of work improves a candidate’s chances to
simply guess the right answer from 25% to 33%.
(6) Markus has a fish tank, where he keeps goldfish. A fish care manual recommends that an
owner change the water in the tank every three weeks. The water should not be completely
replaced, some of it should be left to minimise disturbance to the fish, stones, and waterweed.
The manual recommends changing the water gradually until there’s less than 2% of the original
water left.
Markus removes half of the water from his 51 litre fish tank, then replaces it with new water. He
then repeats this procedure until he reaches the correct amount of original water. Assuming he
waits for the water to mix evenly after each new infusion of water, how many times will Markus
have to repeat this procedure to meet the manual’s standards?
A)
Four times
B)
Six times
C)
Eight times
D)
Seven times
Answer: B
This type of procedure is called a serial dilution. Every repeat of the procedure halves the
amount of water from the original 51 litres. One procedure will leave half the original water, the
next will leave a quarter, a third will leave an eighth, a fourth will leave 1/16, a fifth will leave
1/32, and a sixth will leave 1/64. Since 2% is 1/50, we need six dilutions using this method to
have less than 1/50 of the water left.
(7) Matthew is testing out how long it takes various items of clothing to dry after a wash. He
takes 6 garments as a sample and puts them on a clothesline, outside in the sun. He notes their
material variety, brand, colour, fabric thickness, and later, how long it takes that garment to dry
fully.
Garment
type
Brand
Colour
Thickness
Material
Time
T-shirt
S&M
Brown
1mm
80% cotton, 20%
polyester
98 minutes
T-shirt
Clynch
White
1mm
100% cotton
124
minutes
Hoodie
Guki
Mauve
6mm
50% cotton, 50%
polyester
462
minutes
Sports Sock
S&M
Black
1mm
85% cotton, 10%
polyester, 5% elastic
83 minutes
Hiking Sock
Sportec
Black
5mm
80% cotton, 15%
polyester, 5% elastic
523
minutes
Fleece
Jacket
Sportec
Brown
4mm
100% Polyester
156
minutes
Based on the above data, which of the following statements can be concluded?
I.
Brown materials will dry quicker than white materials.
II.
The thickness of a material is the only factor that determines how quickly it
will dry.
III.
Higher percentages of polyester tended to make materials dry more quickly.
A)
I, II and III
B)
II and III, but not I
C)
I and II, but not III
D)
III only
Answer: D
Let’s look at statement I first. While the brown T- shirt did dry more quickly than the white T-shirt,
we could only decide this statement is correct if there were no other differences between the
garments. Therefore, we cannot conclude that this statement is correct.
Now let’s look at statement II. While the data shows that material thickness is certainly a factor
in how fast things will dry (the hiking sock and hoodie are the two thickest garments and take
the longest and second longest to dry, respectively), the statement says it’s the ONLY factor.
The best example here is the two T-shirts, which differ in what percentage polyester they
contain, and differ in drying times. Since there’s obviously another factor here, this statement is
incorrect.
Finally, let’s look at statement III. When we look at the data, across the table, materials with
higher percentages of polyester do tend to dry more quickly. There’s the t-shirts, which we’ve
already discussed. There’s also the fact that the fleece jacket is nearly as thick as the hiking
sock and hoodie, but dries in dramatically less time. Therefore, we can state that statement III is
correct, making (D) the answer.
(8) Within the human body, there exists the endocrine system, a multitude of glands and
sensors that produce stimulatory or inhibitory hormones, which are then picked up by target
organs, as well as other sensors. The parathalmus, hypocottus, and anterior ventrus are all
hormone-producing organs. LAB, RAD, and ORB are all hormones. The parathalmus releases
LAB, which stimulates the hypocottus to release more RAD, which stimulates the anterior
ventrus to release ORB into the bloodstream, where ORB can travel around the body. ORB
inhibits the release of LAB from the parathalmus and RAD from the hypocottus.
(Excuse the slightly crude diagram!)
If RAD reaches the anterior ventrus, but due to a disorder, the anterior ventrus cannot be
stimulated, which of the following is most likely?
A)
The parathalmus will release less RAD.
B)
The parathalmus will release less LAB.
C)
The hypocottus will release more RAD.
D)
ORB is probably stopping RAD from stimulating the anterior ventrus.
Answer: C
This question is based on the endocrine system for the human body. The author has swapped
out the names of hormones and organs for made up ones, just in case a candidate had a bit of
biology knowledge and could leapfrog the logical reasoning that this question is meant to be
testing.
The question is asking us what will happen if the anterior ventrus cannot be stimulated by RAD.
We know that the anterior ventrus will produce ORB when stimulated. Therefore, we can reason
that without stimulation, the anterior ventrus will not produce ORB.
Having established this, we can then look at what a lack of ORB would do to the system. We
know that, when present, ORB inhibits production of LAB by the parathalmus and also inhibits
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production of RAD by the hypocottus. Therefore, we can reason that without ORB, production of
both LAB (from the parathalmus) and RAD (from the hypocottus) would increase.
Let’s look at how this conclusion fits in with our answer statements. We can discount (A)
immediately, as the parathalmus does not produce RAD at all. Looking at (B), we know the
parathalmus should be releasing more LAB, not less, so we can remove this too. Answer (C) is
consistent with our observations, so it’s probably the answer, but let’s check (D) just in case.
There’s nothing in the passage or diagram to state that ORB is stopping RAD from stimulating
the anterior ventrus, only that it inhibit’s RAD’s production. Therefore we can conclude that (D)
is false and (C) is the correct answer.
(9) One in ten lightbulbs produced by a factory are defective, and do not work. The factory
manager knows this and buys a tester machine to ensure quality control. The machine tests
every lightbulb produced, and spots 80% of the defective bulbs. These bulbs are then rejected
and thrown away. However, the machine is not perfect and also rejects one in ten non-defective
bulbs.
Assuming no further damage occurs to bulbs before they are sold, what percentage of bulbs
sold by the factory are defective?
A)
1%
B)
2.4%
C)
5%
D)
7.3%
Answer: B
The best way to approach this question is to imagine the factory produced a large number of
lightbulbs, for example, 1000, and then to work out the solution from there. This stops your
calculations from going into fractions and decimals, making it a little easier to work with.
Let’s assume the factory produced 1000 bulbs. One in 10 are defective, 9 in 10 are not. So now
we have 100 defective bulbs and 900 working bulbs. The quality check machine removes 80%
of defective bulbs and misses 20%. For our 100 defective bulbs, this means 80 are discarded
and 20 bulbs are going on sale. The machine also discards 1 in 10 working bulbs, so it discards
90 out of 900, leaving us with 810 working bulbs going on sale. 810 + 20 = 830.
So out of the 830 bulbs going on sale, 20 are defective. This means 2/83 of all bulbs sold are
defective. That fraction looks tricky, so let’s leave it there and look at the answer options next.
We have four options and want to start discarding them. Let’s start with the easiest to throw out.
1% of bulbs would mean our end fraction is 1/100, which it’s not. This means we can quickly
discard option (A). By similar process, we can eliminate 5%, as that’s 1/20. This means we can
eliminate option (C).
Even if a candidate ran out of time and had to move on from the question now, you’ve still
increased the probability of picking the correct answer to 1/2 rather than 1/4.
Looking at the remaining two options, (B) is 2.4% and (D) is 7.3%. If we round 2.4 to 2.5 to
make it easier to calculate, then we can get the fraction 1/40, or 2/80. This is very close to the
answer of 2/83, and since we rounded up 2.4 to 2.5, we can assume that 2/80 is slightly
rounded up from the correct answer. Therefore we can conclude (B) is the correct answer.
The kind of maths you’ll be called upon to do in the HPAT can be a little more rough and ready
than your school mathematics course. Many questions will ask for the “best” or “nearest”
answer, and rounding, approximating, and getting a very close answer are all valid techniques in
the HPAT. The exam rewards you for reasoning and critical thinking, not flawless execution of
technique. The only exception are questions where the answer statements can be very similar,
where more accurate calculations are required.
(9b) Factory management is dissatisfied with the percentage of defective bulbs that end up
being sold and feel they should reduce this rate further. They buy a second quality checking
machine and set it up so that the machine checks all bulbs that the first machine rejects. The
new machine accepts every working bulb that was previously discarded, rejecting no working
bulbs. The new machine also accepts one in 10 defective bulbs, rejecting the rest, which are
discarded. The bulbs accepted by this machine are packaged with the other accepted bulbs and
sent to the shops.
What will happen to the rate of defective bulbs ending up on shelves?
A)
It will increase by 0.6% of the total
B)
It will decrease to 0% of the total
C)
It will decrease by 0.3% of the total
D)
It will decrease by 0.4% of the total
Answer: A
Obviously, a candidate who is unable to answer question 10 will be unable to answer this
question. We know that out of our 1000 bulbs, 80 defective ones are rejected, 20 defective ones
are accepted, 90 working ones are rejected, and 810 working ones are accepted.
For the first part of the answer, we need to look at the bulbs that the first machine rejected. Out
of 1000 bulbs, 170 go to the second machine. These are 80 defective ones and 90 working
ones. All 90 working bulbs will be accepted. 8 of the defective bulbs are also accepted. 20 + 8=
28. 810 + 90 = 900. So out of 1000 bulbs, 928 go to the shelf. 28 of these are defective, so our
fraction for how many are defective is 28/928. We can simplify this fraction by dividing the top
and bottom by four, giving us 7/232. This looks like a tricky fraction, but 7/231 is very close to
this fraction and simplifies to 1/33. 1/33 is 3.0303%. Since we rounded our fraction up a little, we
know the correct answer to 7/232 is just under 3.0303%.
Looking at the answer options, it becomes apparent that only one of them is an increase from
our previous answer of 2.4%. A quick sum confirms that adding 0.6% to 2.4% gives us 3%.
We’ve established that the answer should be just under 3.0303%, so 3% fits the bill! Therefore
the answer is (A).
(10) Australians will perhaps be surprised to learn that there are no Parrots or Cockatoos in
Europe, and none in Asia, excepting India, none in Africa north of the Tropic of Cancer, and only
two in North America, and that one of these is rapidly becoming extinct, and that Africa and
India are poor in Parrots. Thus, South America and Australasia alone are left as the lands that
contain these interesting birds in any number. While South America contains the largest
Parrots—the Macaws—all the South American species belong to one family. In the Australian
region six families of Parrots are represented. Four of them are confined to the region, while
only one species of the fifth family (Cockatoos) is found outside the region.
https://www.gutenberg.org/files/34781/34781-h/34781-h.htm
Which of these conclusions cannot be drawn from the above passage?
A)
Australasia and South America are home to the majority of the world’s parrot and cockatoo
species.
B)
Parrots have gone extinct in Africa north of the Tropic of Cancer, only surviving south of it.
C)
Australia has more families of parrots than North America.
D)
India is home to some parrots.
Answer: B
Remember, the question asks which conclusions CANNOT be drawn from the passage. A
classic trick, it will confuse any candidate that fails to read the question carefully, resulting in lost
time or possibly an incorrect answer.
Statement (A) can be confirmed as correct with the statement “South America and Australasia
alone are left as the lands that contain these interesting birds in any number”. They’re
uncommon everywhere else and common in these continents.
Statement (B) could be true, but we don’t know if parrots ever lived north of the Tropic of
Cancer, so there’s no way to know if they became extinct.
Since North America has only two species of parrots, even if they were from separate families,
the most families in North America could have been two, which is less than Australia’s six
families. This means statement (C) is correct.
Statement (D) is easily verifiable. The passage states parrots cannot be found in Asia except for
India. Therefore it can be assumed India is home to some parrots.
(11) The following passage relates to the swallow-tail butterfly.
“It appears that this butterfly was once widely distributed throughout England, having been
recorded as common in various counties, and has also been taken in Scotland and Ireland; but
it is now almost exclusively confined to the fens of Cambridgeshire, Huntingdonshire, and
Norfolk. Occasionally we hear of the capture of single specimens quite outside these localities,
sometimes even in most unlikely spots, where its food plant does not abound. But we know that
the swallow-tail is a general favourite with entomologists, and that it is sent in the pupal state, by
post, to all parts of the kingdom; so that the occasional capture of the insect far beyond the
borders of its haunts is probably the outcome of an escape from prison, or of the
tender-heartedness of some lover of nature who could not bear to see such a beautiful creature
deprived of its short but joyous, sunny flight.”
https://www.gutenberg.org/files/34131/34131-h/34131-h.htm#Page_139
What conclusions can be drawn from the above passage?
I.
Swallow-tail butterflies used to be more geographically widespread than
they are now.
II.
Swallow-tail butterflies are only found naturally in the wild in the fens of
Cambridgeshire, Huntingdonshire, and Norfolk.
III.
Often, entomologists will release swallow-tail butterflies to appreciate their
beauty.
A)
I, II and III
B)
I and III
C)
I only
D)
II and III
Answer: C
Let’s examine each of the statements.
Statement I states that swallow tailed butterflies used to be more geographically widespread
than they are now. This is confirmed by the passage stating that they used to be widely
distributed throughout England, and even Scotland and Ireland, but are only found almost
exclusively in three specific places now. Therefore, this statement is correct. This allows us to
eliminate option (D) as an answer.
Statement II appears correct at first glance, echoing the place names present in the passage’s
first sentence. However, the statement says that they are ONLY found naturally in the fens of
Cambridgeshire, Huntingdonshire, and Norfolk, whereas the passage says “almost exclusively”.
It’s a small difference, and easy to miss, but it renders statement II incorrect. Therefore, we can
eliminate option (A) as an answer, as well as eliminating (D) which we’d eliminated before.
Statement III also seems correct at first glance. The last part of the passage verges on the
whimsical, which sounds awfully convincing to candidates, who might imagine that
entomologists will share their feelings. However, this is Section 1 of the HPAT! There’s no room
for being swayed by poetic language here! Since these butterflies are only occasionally found in
locations where it can be assumed it escaped or was released, but they’re frequently sent by
post “to all parts of the kingdom” for entomologists. If entomologists releasing these butterflies
occurred “often”, one would reasonably expect to find the butterflies in the wild more often than
“occasionally”. Therefore, statement III is incorrect and we can eliminate option (B) as an
answer, leaving us with (C) as the correct option.
(11a) “The food plants of the swallow-tail are the milk parsley or hog's fennel (Peucedanum
palustre), cow-parsnip (Heracleum sphondylium), and the wild angelica (Angelica sylvestris); but
in confinement it will also grudgingly partake of rue and carrot leaves.”
Taking this passage into consideration, in addition to the previous passage, which of the
following conclusions can be drawn?
A)
Swallow-tail butterflies are known pests to carrot farmers in Cambridgeshire,
Huntingdonshire, and Norfolk.
B)
The wild angelica is the favourite food of the swallow-tail butterfly.
C)
Given the choice, a wild swallow-tail will choose rue leaves over cow-parsnip.
D)
Milk parsley, cow-parsnip and the wild angelica can be found growing wild in the fens of
Cambridgeshire, Huntingdonshire, and Norfolk.
Answer: D
Since it’s observed that the swallow-tail butterfly will only partake of rue and carrot leaves if no
other food is available, we can remove (A) and (C) as options. Since they have no appetite for
carrot leaves, they would not be a pest to carrot farmers. Similarly, the passage indicates that
the swallow-tail prefers cow-parsnip to rue leaves.
Examining (B), while it is true that the swallow-tail eats the wild angelica, there’s nothing to
suggest it’s its favourite over the others. Therefore we can eliminate option (B)
Finally, option (D) suggests that the wild plants the swallow-tail eats can be found in its natural
habitat, a perfectly logical conclusion. Therefore, the answer is (D).
The following statement relates to the evolution of certain species of amphibians.
In both Anura and Urodela the skull is short, broad, relatively flat, with reduced pterygoids that
diverge laterally from the parasphenoids leaving large interpterygoid vacuities, and with large
orbits. (These statements do not apply to certain larval or perennibranchiate forms.) The skull in
both orders has gained a number of primitive dermal bones in the posterior part; these are:
basioccipital, supraoccipital, postparietal, intertemporal, supratemporal, and tabular. The
exoccipitals form the two condyles but there are no foramina for the 11th and 12th nerves since
these are not separate in modern Amphibia. The opisthotic is missing in all except Proteidae.
Although the skull is normally autostylic, a movable basipterygoid articulation is present among
Hynobiid salamanders and in at least the metamorphic stages of primitive frogs, and therefore
should be expected in their ancestors.
(15)
Which of these sets of bones can be found in the posterior part of the amphibian skull?
A)
Postparietal, exoccipital, supraoccipital
B)
Tabular, basioccipital, opisthotic
C)
Intertemporal, opisthotic, supratemporal
D)
Tabular, postparietal, supraoccipital
Answer: D
There’s an awful lot of information here, and the words the candidate is looking for are long and
complicated sounding. However, all that’s being asked of the candidate is to pick the correct set
of words from a sentence in the middle if the passage. The stumbling block here lies with the
candidate simply getting overloaded by complicated information, and not focusing in on what the
question is asking.
A quick glance at the sentence “The skull in both orders has gained a number of primitive
dermal bones in the posterior part; these are: basioccipital, supraoccipital, postparietal,
intertemporal, supratemporal, and tabular” lets us remove options (A), (B), and (C). These
contain the names of bones not found here, so we can eliminate them all at once. Therefore, the
answer is (D).
(16)
Which of the following statements are true?
I.
It’s unusual for amphibian skulls to be autostylic
II.
Modern amphibians have separate foramina for their 11th and 12th nerves
III. Modern frogs should have movable basipterygoid articulation.
A)
III only
B)
I only
C)
II and III
D)
I, II and III
Answer: A
The passage’s information is no less complex, but, once again, a candidate should be able to
find the information that they’re looking for.
Let’s look at statement I, stating it’s unusual or amphibian skulls to be autostylic. The final
sentence in the passage states the opposite, so we can discount statement I, thereby
eliminating answer options (B) and (D).
Statement II is even easier to discount, the passage states that the nerves are not separate
about halfway through. Therefore we can eliminate statement II, and therefore option (C).
This means (A) is the answer.
The following graph shows information of one factor (x) vs another factor (y). It also shows the
line of best fit, for all points present. In other words, the line drawn is the average line, taking
into account all points on the graph
(17)
Which of the following points could best be described as a statistical outlier?
A)
R
B)
A
C)
D
D)
S
Answer: D
This is a basic graph interpretation question. Point S is furthest from the line of best fit and is the
best of the points presented in the answer options to be described as a statistical outlier. Points
R, A and D are all less than five units away from the line of best fit, whereas S is far further.
(18)
Which points, if eliminated, would cause the most increase in slope of the line of best fit?
A)
L, I, B
B)
K, R, J
C)
A, C, M
D)
D, K, Q
Answer: A
A less mathematical way to think about this problem is to imagine every point is “pulling” on the
line in an attempt to draw it closer.
Let’s look at points L, I and B. L is a statistical outlier and is “pulling” the line towards the top left
of the image. B is doing the same, but not to the same extent. Point I is on the other side of the
line and is “pulling” downward and to the right, but only by a little bit. Therefore, removing these
points would allow the left side of the line to move downward, increasing the slope. To be sure
this is causing the most increase in slope, let’s check the others.
Let’s look at K, R and J. Removing these points would let the right side of the line fall down,
decreasing the slope. Therefore, this option is incorrect.
Points A, C and M would let the left side of the line move upward, also decreasing the slope.
Therefore this option is incorrect.
Let’s look at points D, K and Q. D and Q are almost exactly mirrored on the line, and K is on the
line. If these points were removed, the difference on the line would be negligible, if it moved at
all.
Given that options (B) and (C) would decrease the slope, and option (D) would have no effect,
it’s obvious (A) is the correct answer.
Below is a family tree of the British royal family. The throne is passed down through the
generations using the following rules.
1)
The throne passes to the oldest surviving male child of the monarch at the time of the
reigning monarch’s death.
2)
If the reigning monarch has no male children, then it passes to the oldest female child.
3)
If the reigning monarch has no children, then it passes to the monarch’s oldest male sibling.
4)
If the reigning monarch has no male siblings, then it passes to the monarch’s oldest female
sibling.
If there are no siblings to be found, then rules are repeated for parental siblings, then first
cousins, then parental cousins, then second cousins, and so on.
The order of people left to right, on a line, shows the order they were born in, with the oldest
on the left.
(19)
If King Edward VII died in childhood and never became king, who would have inherited the
throne instead of him?
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A)
Prince Ernest
B)
Princess Victoria
C)
Princess Alexandra
D)
Prince Alfred
Answer: D
Let’s look at our options. Option (A), Ernest, is two generations older than Edward VII, and
would be quite far down the line of succession as a result. Option (B), Princess Victoria, is
Edward VII’s oldest sibling, but is not male. Therefore, she is not next in line, and would only
inherit the throne after the death of all her brothers (and their descendants). Option (C),
Princess Alexandra is Edward’s wife, but there’s nothing in the rules about passing the throne to
spouses (besides, Edward died in childhood, and so never married in the first place!)
This leaves us with option (D) as an answer. A quick check confirms that Prince Alfred is
Edward VII’s oldest male sibling, which would leave him as next in line to the throne.
(20)
Princess Elizabeth is not content with her lot in life and decides to assassinate her siblings in
order to become the next in line to the throne. Assuming her parents, King George III and
Queen Charlotte are alive, and at least two of her siblings died as children, what is the minimum
and maximum number of siblings she must assassinate to inherit the throne?
A)
9 minimum, 10 maximum
B)
11 minimum, 13 maximum
C)
10 minimum, 11 maximum
D)
9 minimum, 11 maximum
Answer: D
Elizabeth is female and must therefore remove all male heirs to the throne, as well as female
heirs older than her. A quick count reveals there are nine male heirs and two female heirs that
are older than her. Therefore, if it were her youngest sisters that died in childhood, she would
need to remove 11 other options for the throne. If it were some of her older siblings, she would
be spared from removing them herself, so 9 at minimum. With 9 minimum and 11 maximum, the
answer is (D).
Timmy, Tommy, Tina, and Toby all enter a sweetshop and purchase sweets. Upon exiting the
shop, they are pursued by the shopkeeper who has noticed he is missing an extra pack of
sweets. He accuses them of shoplifting.
Timmy says “It wasn’t me, I didn’t see who did it.”
Tommy says “I saw her! It was Tina!”
Tina says “Liar! Tommy’s trying to cover up for Toby, he took the sweets!”
Toby says “I didn’t steal anything! It wasn’t me.”
(21)
Assuming only one of them is lying, which one took the sweets?
A)
Tommy
B)
Tina
C)
Toby
D)
Timmy
Answer: B
For this interaction to make sense, we need three statements to be true, and only one to be a
lie.
A good place to start for these questions is looking for statements that directly contradict each
other. Tommy accuses Tina, while Tina accuses Toby. Toby denies any wrongdoing. Therefore
we can say that Tommy and Tina contradict each other, and Toby and Tina contradict each
other.
If Timmy’s statement was false, then the other three would have to be true. As these contradict
each other, we can say that Timmy is telling the truth. Therefore we can remove option (D).
If Tommy’s statement was false, then both Tina and Toby’s statements would be true. However,
these contradict each other, and cannot both be true. Therefore, Tommy’s statement cannot be
false. We can remove option (A) as an answer.
If Tina’s statement was false, then the other three would be true. As none of these contradict
each other (Tommy accuses Tina, and both Toby and Timmy deny any wrongdoing), this makes
sense logically. Therefore, we can conclude that Tina is lying and that the answer is (B).
Below is a table detailing various brands of materials, as well as their cost, tensile strength and
compressive strength.
Material
Cost
Tensile Strength
Compressive Strength
Tempered Steel
$40/metre
10
8
Tatara Steel
$45/metre
12
8
Precast Concrete
$20/sq. metre
6
14
Ready-set Concrete
$23/sq. metre
9
12
Titan Concrete
$28/ sq. metre
10
13
Smith’s Steel
$30/metre
7.5
7
Reforged Steel
$24/half metre
17
15
Andesite Concrete
$30/sq. metre
10
11
(22)
An engineer is attempting to build a bridge across a busy highway. She needs one type of
concrete and one type of steel, to be used throughout the bridge. The bridge materials need a
tensile strength of no less than 9, and a compressive strength of no less than 10. Since the
engineer wants to minimise costs when building the bridge, which materials should she use?
A)
Ready-set Concrete and Tatara Steel
B)
Reforged Steel and Andesite Concrete
C)
Reforged Steel and Ready-set Concrete
D)
Titan Concrete and Reforged Steel.
Answer: C
When confronted with a large amount of data, and a question involving combinations such as
this one, it’s often a good idea to begin with the answers and then check back with the data.
The first step here is to check which combinations of materials fit the requirements, then worry
about cost later.
Ready-set concrete has a TS of 9 and CS of 12. This fits requirements. Tatara Steel has a TS of
10 but a CS of only 8, rendering it unusable here. This means option (A) is invalid.
Reforged Steel has a TS of 17 and a CS of 15. This fits requirements. Andesite Concrete has a
TS of 10 and a CS of 11. As this falls within the requirements too, we can say this (B) is a
possible answer.
Examining option (C), we already know Reforged Steel fits requirements, as does Ready-set
concrete. We can also put down (C) as a possible answer.
Titan Concrete fits requirements too, with a TS of 10 and CS of 13. Since we know Reforged
Steel also fits requirements, we can put down (D) as a possible answer.
So now we have three suitable combinations of materials, we need to find which is cheapest. All
suitable combinations share Reforged Steel as the steel, so we need to look at the cheapest
concrete. A quick check shows this is Ready-set concrete, meaning C is the correct answer.
(23)
The engineer reworks the bridge design to be more weather-resistant. Now, she needs steel
with a tensile strength of no lower than 11, and concrete with a compressive strength no lower
than 13. The compressive strength of the steel and the tensile strength of the concrete are of no
consequence. Assuming she needs to buy 100 metres of steel and 100 square metres of
concrete to construct the bridge, how much what is the price difference for this new design?
A)
$300 cheaper
B)
$600 cheaper
C)
$1800 more expensive
D)
$500 more expensive
Answer: B
The cheapest steel to use for the purposes required is Tatara Steel, with a TS of 12. The
cheapest concrete that fits the requirements is Precast Concrete, with a CS of 14.
100 units of Tatara Steel would cost $4500, compared to $4800 for 100 units of Reforged Steel
(look carefully, Reforged Steel is sold by the half metre, different to the rest). This is $300
cheaper than before.
100 units of Precast Concrete would cost $2000, compared to $2300 for Ready-set Concrete.
This is $300 cheaper than before.
In total, the new design costs $600 less to build than the previous one. This makes (B) the
correct answer.
Adam watches a video of a man throwing a boomerang. The man leans back, then throws his
weight forward, whipping his arm ahead of him and flicking his wrist before letting go of the
boomerang. It flies in a smooth arc before coming back to the man’s location, where he catches
it effortlessly.
Adam says “I could do that too, if I was as tall as he is”.
(24)
What is the flaw in Adam’s reasoning?
A)
Being short is preferable to being tall when throwing a boomerang
B)
Performance of a task like this is related to practice, not height
C)
Throwing a boomerang is a skill that Adam could never master, regardless of his height
D)
None, his reasoning is completely sound
Answer: B
One thing to remember here is that within the HPAT, a candidate will only be tested on what’s
presented within the question. In other words, you don’t need to know anything about
boomerang throwing specifically. Here, you’re just being asked to apply logic to the above
statements.
Let’s examine statement (A), that being short is preferable to being tall when throwing a
boomerang. While this would be opposed to Adam’s statement if true, it could not be described
as a flaw in his reasoning, rather just that he doesn’t have this piece of knowledge. That’s
assuming the statement is true in the first place, which there’s no indication of! We can therefore
discount this answer option.
Looking at statement (B), it seems more reasonable. The task has multiple physical steps that
must be completed exactly, the kind of task that needs to be practiced. Stating that this ability is
related to height, not practice is illogical.
Looking at statement (C), it looks illogical even at first glance. It states that Adam could never
hope to throw a boomerang correctly. There’s nothing to state that Adam would be unable to
throw a boomerang, except Adam himself, which the question is based on. We can therefore
discount option (C).
Finally, statement (D) is incorrect for the same reasons that (B) is correct.
Laura possess thirteen wooden orbs, each identical in appearance. All are identical in weight,
except for one orb. This orb is very slightly heavier than the others, due to a small metal core.
This difference is not enough to notice when held in hand, but enough to tip a scales.
(25)
With only a simple scales (pictured below), what is the maximum number of uses Laura needs
to determine which is the heavy ball for absolute certainty?
A)
2
B)
3
C)
4
D)
5
Answer: B
First, weigh four orbs against another four orbs. If they’re even, then weigh two of the remaining
five versus another two of the remaining five. If they’re even, the remaining orb is heavy. (2
uses) If they’re not, weigh the two orbs on the heavier side against each other to find the heavy
one (3 uses).
If the initial 4v4 weighing comes out uneven, then weigh two of the heavier side’s orbs against
the other two of the heavier side’s orbs. This determines which set is heavier. A final weighing
between the two of the heavier set will determine the heavier orb (3 uses).
The maximum number of uses necessary is three, therefore the answer is (B).
Using the same scales, Laura is presented with twelve new orbs. Eleven are of identical weight
but the twelfth is of a slightly different weight. It is unknown whether this orb is slightly heavier or
slightly lighter than the other eleven.
(26)
How many uses of the scales does Laura need to determine which is the odd ball out, and
whether it’s heavier or lighter?
A)
2
B)
3
C)
4
D)
4+
Answer: B
Like the previous question, Laura weigh four balls vs another four. If they balance, then the odd
ball out is in the final four. Weigh three of the final four against three from the first 8. If they
balance, then the odd ball is 12 and a third weighing can determine whether it’s heavier or
lighter. If the three vs three weighing doesn’t balance, then Laura knows the odd ball is within
the three taken from the group of 4 earlier. Within these, she can use one more weighing to
determine the odd ball.
If the initial 4v4 weighing doesn’t balance, then we know the other 4 balls are all even. Using
this information in the same way as above, we can establish the odd ball out using the same
methods described above.
A bakery sells various baked goods. The staff begin baking at 6 AM, while the bakery opens to
customers at 7 AM. The shop closes to customers at 12 PM, with the staff finishing baking an
hour before. The manager of the bakery has the amount of baked goods sold each day down to
an exact science, and as a result all food baked is sold per day. No customer who comes in to
buy something finds their chosen product is out of stock.
Every customer buys only one type of item and never buys any more than three of that item at a
time, though most customers buy less.
Data about the food sales on a certain day is detailed below, with some data omitted.
Food
Number produced
per hour
No. of customers
Total sold that day.
Plain Croissant
25.2
98
126
Cake Slice
18
42
90
Danish Pastry
23.2
(W)
116
Apple Pie
30
42
150
Blueberry Muffin
18.8
73
94
Almond Croissant
(X)
134
210
Lemon Slice
20.8
47
104
Chocolate Tart
(Y)
19
(Z)
Blackcurrant Tart
6
28
30
Raspberry Muffin
21.2
78
106
Meringue Cupcake
32.6
102
163
(27)
What is the correct value for (X) on the table above?
A)
30
B)
35
C)
37
D)
42
Answer: D
This is a simple mental maths question, only requiring a candidate to divide 210 by 5 (the
number of hours the staff actually bake for). Candidates may trip up and miscalculate the
number of hours they bake for, resulting in an incorrect answer.
(28)
What’s the minimum value that (W) could stand for?
A)
78
B)
116
C)
39
D)
58
Answer: C
Even though the stimulus states that most customers who come in buy less than three products,
the question asks you for the minimum possible value of W. Therefore, you can disregard this
statement and work with the minimum values only. This means each customer would have to
buy the maximum number of goods (3). The information about the maximum purchase amounts
is a fixed rule of the question, not a misleading statement like the one mentioned earlier.
A quick sum determines that 116/3 is 38 with 2 remaining pastries, so 39 customers required.
This is the minimum possible value for W, therefore (C) is the correct answer.
(29)
Calculate the minimum and maximum number of chocolate muffins are produced per hour.
A)
4.8 and 24.0
B)
3.8 and 11.4
C)
3.8 and 11.2
D)
4.8 and 11.2
Answer: B
This information is presented by the placeholder Y in the table.
To calculate the possible values of Y, we first need the possible values of Z. We can then divide
the total number of muffins produced by 5 (hours baking) to get number produced per hour. The
maximum value for Z is 57, assuming each customer buys three muffins. 57/5 is 11 and 2/5, so
11.4 is the maximum value for Y.
If each customer only bought one muffin, then we can divide 19 by 5 and end up with 3 and 4/5,
so 3.8 is the minimum value for Y. This only fits with answer option (B), so it’s correct.
The bakery’s manager decides to introduce a new product, the Vanilla Muffin. He calculates
that, to meet demand exactly, the rate of muffin production in the bakery will increase by 40%.
(30)
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