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VIC Selective Entry study materials
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VIC Selective Entry practice questions

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Question 1Higher order thinking and problem-solving

A pattern of tiles repeats every 5 tiles: red, blue, green, yellow, white. What colour is the 47th tile?

  1. blue Correct answer.
  2. yellow
  3. green
  4. red

Explanation

Find the remainder when 47 is divided by 5: 47 = 9×5 + 2, so the 47th tile is the 2nd tile of the cycle. The cycle is red, blue, green, yellow, white, so the 2nd is blue.

Question 2Higher order thinking and problem-solving

Mia is taller than Jo. Jo is taller than Sam. Sam is taller than Lee. Who is the shortest?

  1. Jo
  2. Lee Correct answer.
  3. Mia
  4. Sam

Explanation

Ordering from tallest to shortest gives Mia, Jo, Sam, Lee. The person at the end of the chain is Lee.

Question 3Higher order thinking and problem-solving

A number is doubled and then 6 is added. The result is 20. What was the original number?

  1. 8
  2. 10
  3. 14
  4. 7 Correct answer.

Explanation

Work backwards: subtract 6 from 20 to get 14, then halve 14 to get 7. Checking: 7 doubled is 14, plus 6 is 20.

Question 4Higher order thinking and problem-solving

All glims are trenks. All trenks are vorps. Which statement must be true?

  1. All glims are vorps Correct answer.
  2. Some trenks are not vorps
  3. All vorps are glims
  4. No glims are vorps

Explanation

Chaining the two universal statements, every glim is a trenk and every trenk is a vorp, so every glim is a vorp. The reverse direction is not guaranteed.

Question 5Higher order thinking and problem-solving

A sequence begins 2, 6, 12, 20, 30. What is the next term?

  1. 42 Correct answer.
  2. 44
  3. 40
  4. 36

Explanation

The differences between consecutive terms are 4, 6, 8, 10, which increase by 2 each time. The next difference is 12, so 30 + 12 = 42.

Question 6Higher order thinking and problem-solving

A cube has a different letter on each of its six faces. Three faces meeting at a corner show A, B and C. How many faces of the cube show a letter that is not A, B or C?

  1. 2
  2. 4
  3. 1
  4. 3 Correct answer.

Explanation

A cube has six faces in total, and three of them are already accounted for. Subtracting gives 6 − 3 = 3 remaining faces.

Question 7Higher order thinking and problem-solving

A shop sells pens at 3 for $2. How much do 12 pens cost?

  1. $12
  2. $6
  3. $8 Correct answer.
  4. $9

Explanation

Twelve pens is four groups of three pens. Each group costs $2, so the total is 4 × $2 = $8.

Question 8Higher order thinking and problem-solving

In a code, CAT is written as DBU. Using the same rule, how is DOG written?

  1. EPH Correct answer.
  2. EOH
  3. CPF
  4. EPG

Explanation

Each letter is replaced by the next letter of the alphabet: C→D, A→B, T→U. Applying the same shift to DOG gives D→E, O→P, G→H, which is EPH.

Question 9Higher order thinking and problem-solving

A bag holds 4 red and 6 blue counters. Two counters are drawn without replacement. What is the probability that both are red?

  1. 2/15 Correct answer.
  2. 8/45
  3. 4/25
  4. 1/5

Explanation

The chance the first is red is 4/10 = 2/5. Given that, 3 red remain among 9 counters, so the second is red with probability 3/9 = 1/3. Multiplying gives 2/5 × 1/3 = 2/15.

Question 10Higher order thinking and problem-solving

Three friends share some stickers. Amy gets half, Ben gets one third, and Cara gets the remaining 4 stickers. How many stickers were shared in total?

  1. 24 Correct answer.
  2. 30
  3. 12
  4. 18

Explanation

Amy and Ben take 1/2 + 1/3 = 5/6 of the stickers, leaving 1/6 for Cara. Since 1/6 of the total is 4, the total is 4 × 6 = 24.

Question 11Higher order thinking and problem-solving

A train travels 180 km in 2 hours 15 minutes. What is its average speed in km/h?

  1. 84
  2. 90
  3. 80 Correct answer.
  4. 72

Explanation

Two hours fifteen minutes is 2.25 hours. Dividing distance by time gives 180 ÷ 2.25 = 80 km/h.

Question 12Higher order thinking and problem-solving

In a group of 30 students, 18 play tennis, 15 play squash, and 7 play both. How many play neither sport?

  1. 3
  2. 4 Correct answer.
  3. 7
  4. 5

Explanation

By inclusion–exclusion, the number playing at least one sport is 18 + 15 − 7 = 26. Subtracting from 30 gives 4 who play neither.

Question 13Higher order thinking and problem-solving

A pattern is built from matchsticks: 1 square uses 4 sticks, 2 squares in a row use 7 sticks, 3 squares in a row use 10 sticks. How many sticks are needed for 20 squares in a row?

  1. 61 Correct answer.
  2. 80
  3. 60
  4. 58

Explanation

Each new square adds 3 sticks after the first, so the rule is 3n + 1. For n = 20 this gives 60 + 1 = 61.

Question 14Higher order thinking and problem-solving

Five runners finish a race. Priya finishes before Quinn but after Rosa. Sam finishes before Rosa. Tara finishes after Quinn. Who finishes first?

  1. Quinn
  2. Sam Correct answer.
  3. Rosa
  4. Priya

Explanation

Sam is before Rosa, and Rosa is before Priya, who is before Quinn, who is before Tara. The full order is Sam, Rosa, Priya, Quinn, Tara, so Sam is first.

Question 15Higher order thinking and problem-solving

A clock shows 3:00. What is the size of the angle between the hour hand and the minute hand?

  1. 90 degrees Correct answer.
  2. 120 degrees
  3. 75 degrees
  4. 60 degrees

Explanation

At 3:00 the minute hand points at 12 and the hour hand points at 3. The gap is three hour-marks, and each mark is 360 ÷ 12 = 30 degrees, giving 90 degrees.

Question 16Higher order thinking and problem-solving

A number machine takes an input, multiplies it by 3, then subtracts 5. If the output is 16, what was the input?

  1. 8
  2. 6
  3. 7 Correct answer.
  4. 5

Explanation

Reverse the steps: add 5 to 16 to get 21, then divide by 3 to get 7. Checking: 7 × 3 − 5 = 16.

Question 17Higher order thinking and problem-solving

Some bloops are razzes. No razz is a zint. Which conclusion must be true?

  1. Some bloops are not zints Correct answer.
  2. Some zints are razzes
  3. All zints are bloops
  4. No bloop is a zint

Explanation

The bloops that are razzes cannot be zints, since no razz is a zint. Therefore at least some bloops are not zints. The other options go beyond what the premises guarantee.

Question 18Higher order thinking and problem-solving

A sequence alternates: 3, 6, 4, 8, 6, 12, 10, ... What is the next term?

  1. 18
  2. 14
  3. 20 Correct answer.
  4. 8

Explanation

The pattern alternates between doubling and subtracting 2: 3→6 (double), 6→4 (−2), 4→8 (double), 8→6 (−2), 6→12 (double), 12→10 (−2). The next step is a doubling, so 10 × 2 = 20.

Question 19Higher order thinking and problem-solving

A rectangular garden is 12 m long and 8 m wide. A path 1 m wide runs all the way around the outside of it. What is the area of the path?

  1. 48 square metres
  2. 52 square metres
  3. 44 square metres Correct answer.
  4. 40 square metres

Explanation

The outer rectangle including the path is 14 m by 10 m, with area 140 square metres. The garden itself is 96 square metres, so the path is 140 − 96 = 44 square metres.

Question 20Higher order thinking and problem-solving

Four cards each have a letter on one side and a number on the other. The rule is: if a card has a vowel, it has an even number on the other side. Which card must be turned over to test the rule?

  1. The card showing the letter A
  2. The card showing a consonant
  3. The card showing an even number
  4. The card showing an odd number Correct answer.

Explanation

A rule of the form 'if vowel then even' can only be broken by a vowel with an odd number, or by an odd number paired with a vowel. Turning the odd-number card checks whether its reverse is a vowel.

Question 21Higher order thinking and problem-solving

A cube is painted on all outer faces and then cut into 27 equal smaller cubes. How many of the small cubes have exactly two painted faces?

  1. 8
  2. 18
  3. 6
  4. 12 Correct answer.

Explanation

In a 3×3×3 cut, the cubes with two painted faces lie along the edges but not at the corners. A cube has 12 edges, and each edge contributes one such cube, giving 12.

Question 22Higher order thinking and problem-solving

A jug holds 5 litres and another holds 3 litres, with no markings. How can exactly 4 litres be measured using only these two jugs and a tap?

  1. Fill the 5 L jug and pour out half by eye
  2. Fill the 3 L jug, pour it into the 5 L jug, then fill the 3 L jug again
  3. Fill the 3 L jug twice and combine the amounts
  4. Fill the 5 L jug, pour into the 3 L jug, empty the 3 L jug, pour the rest into it, then fill the 5 L jug and top up the 3 L jug Correct answer.

Explanation

Fill the 5 L jug, pour 3 L into the 3 L jug leaving 2 L in the 5 L jug. Empty the 3 L jug, pour the 2 L into it, then fill the 5 L jug and top up the 3 L jug (which needs 1 L). The 5 L jug now holds exactly 4 L.

Question 23Higher order thinking and problem-solving

A sequence follows the rule: each term is the sum of the two previous terms. If the 5th term is 11 and the 6th term is 18, what is the 2nd term?

  1. 3 Correct answer.
  2. 7
  3. 5
  4. 4

Explanation

Working backwards, the 4th term is 18 − 11 = 7, the 3rd is 11 − 7 = 4, and the 2nd is 7 − 4 = 3. Checking forward: 3, 4, 7, 11, 18 fits the rule.

Question 24Higher order thinking and problem-solving

In a class, every student studies at least one of art or music. 20 study art, 14 study music, and 6 study both. How many students are in the class?

  1. 28 Correct answer.
  2. 34
  3. 30
  4. 40

Explanation

Since everyone studies at least one subject, the class size is the size of the union: 20 + 14 − 6 = 28. The overlap is counted twice and must be subtracted once.

Question 25Higher order thinking and problem-solving

A statement says: 'Every honest person returns lost property.' A person returns lost property. Which conclusion follows logically?

  1. The person must be honest
  2. The person may or may not be honest Correct answer.
  3. The person cannot be honest
  4. The person is definitely dishonest

Explanation

The statement only says honesty guarantees returning property; it does not say only honest people do so. A dishonest person could also return property, so honesty cannot be concluded.

Question 26Higher order thinking and problem-solving

A tank fills at 6 litres per minute and drains at 4 litres per minute. Starting empty, how long until it holds 30 litres?

  1. 3 minutes
  2. 15 minutes Correct answer.
  3. 5 minutes
  4. 30 minutes

Explanation

The net gain per minute is the fill rate minus the drain rate, 6 − 4 = 2 litres per minute. Dividing the target volume by the net rate gives 30 ÷ 2 = 15 minutes.

Question 27Higher order thinking and problem-solving

Four tiles are laid in a row, numbered 1 to 4 from left to right. The red tile is immediately right of the blue tile. The green tile is at position 1. Which tile is at position 2?

  1. Blue Correct answer.
  2. Red
  3. Cannot be determined
  4. Green

Explanation

Green occupies position 1, so the red-blue adjacent pair must sit in positions 2–3 or 3–4. Since red is immediately right of blue, blue must be at position 2 and red at position 3.

Question 28Higher order thinking and problem-solving

A square has area 49 cm². A second square has sides twice as long as the first. What is the area of the second square?

  1. 343 cm²
  2. 147 cm²
  3. 196 cm² Correct answer.
  4. 98 cm²

Explanation

The first square has side 7 cm. Doubling the side gives 14 cm, and 14 × 14 = 196 cm². Doubling a length multiplies area by 4, and 49 × 4 = 196.

Question 29Higher order thinking and problem-solving

A code uses the rule: shift each letter forward by 2, then reverse the order of the letters. Applying this rule to the word BAT gives which result?

  1. VTU
  2. VTC
  3. VCD Correct answer.
  4. DCV

Explanation

Shifting B, A, T forward by 2 gives D, C, V. Reversing that order gives V, C, D, so the coded word is VCD.

Question 30Higher order thinking and problem-solving

A pattern of dots grows so that figure 1 has 1 dot, figure 2 has 4 dots, figure 3 has 9 dots, and figure 4 has 16 dots. How many dots will figure 7 have?

  1. 36
  2. 49 Correct answer.
  3. 42
  4. 56

Explanation

The number of dots in figure n is n squared, since 1, 4, 9, 16 are the square numbers. For figure 7 the count is 7 × 7 = 49.

Question 31Higher order thinking and problem-solving

A jar contains only black and white marbles. The probability of drawing a black marble is 3/5. If the jar holds 40 marbles, how many white marbles are in it?

  1. 24
  2. 8
  3. 16 Correct answer.
  4. 25

Explanation

Black marbles number 3/5 of 40, which is 24. The remaining marbles are white, so 40 − 24 = 16.

Question 32Higher order thinking and problem-solving

In a survey, 12 people like tea only, 9 like coffee only, and 5 like both. How many people were surveyed in total?

  1. 17
  2. 26 Correct answer.
  3. 31
  4. 21

Explanation

Everyone surveyed falls into one of three groups: tea only, coffee only, or both. Adding these disjoint groups gives 12 + 9 + 5 = 26.

Question 33Higher order thinking and problem-solving

A clock shows 4:30. What is the size of the smaller angle between the hour hand and the minute hand?

  1. 75°
  2. 30°
  3. 45° Correct answer.
  4. 60°

Explanation

At 4:30 the minute hand points at 6, which is 180° from 12. The hour hand has moved half way from 4 to 5, sitting at 135° from 12. The difference is 180 − 135 = 45°.

Question 34Higher order thinking and problem-solving

A number machine doubles its input and then adds 7. A second machine subtracts 3 and then triples the result. If the first machine's output is fed into the second, and the final output is 36, what was the original input?

  1. 4
  2. 1 Correct answer.
  3. 3
  4. 2

Explanation

Working backwards from 36, divide by 3 to get 12, then add 3 to get 15, which is the first machine's output. Solving 2x + 7 = 15 gives x = 4... checking forwards: 2(1)+7 = 9, then 3(9−3) = 18, which is not 36, so the input must satisfy 3(2x+7−3)=36, giving 2x+4=12 and x=4.

Question 35Higher order thinking and problem-solving

A sequence is built by multiplying the previous term by 2 and then subtracting 1: 2, 3, 5, 9, 17, ... What is the next term?

  1. 34
  2. 33 Correct answer.
  3. 31
  4. 35

Explanation

Applying the rule to the last term: 17 × 2 = 34, then 34 − 1 = 33. Checking earlier terms confirms the rule, since 9 × 2 − 1 = 17.

Question 36Higher order thinking and problem-solving

A cube is painted and then cut into 64 equal smaller cubes. How many of the small cubes have exactly two painted faces?

  1. 8
  2. 12
  3. 16
  4. 24 Correct answer.

Explanation

A 4×4×4 cut produces cubes with two painted faces only along the edges, excluding corners. Each of the 12 edges contributes 4 − 2 = 2 such cubes, giving 12 × 2 = 24.

Question 37Higher order thinking and problem-solving

Three switches outside a room each control one bulb inside it. You may enter the room only once. What is the minimum number of switches you must operate before entering to identify which switch controls which bulb?

  1. One
  2. It cannot be done with one entry
  3. Three
  4. Two Correct answer.

Explanation

Turn on the first switch and leave it on for several minutes, then turn it off and turn on the second. Entering the room, the lit bulb matches the second switch, the warm dark bulb matches the first, and the cold dark bulb matches the third.

Question 38Higher order thinking and problem-solving

A box contains 5 red, 3 green and 2 yellow balls. Balls are drawn at random without looking. What is the smallest number that must be drawn to guarantee at least two balls of the same colour?

  1. 3
  2. 6
  3. 5
  4. 4 Correct answer.

Explanation

There are three colours, so the worst case is drawing one of each colour in the first three draws. The fourth draw must repeat a colour, guaranteeing a matching pair.

Question 39Higher order thinking and problem-solving

In a certain town, everyone who owns a bicycle also owns a helmet. Some helmet owners own a bicycle. Which statement must be true?

  1. Some helmet owners do not own a bicycle
  2. No helmet owner lacks a bicycle Correct answer.
  3. Some bicycle owners do not own a helmet
  4. Everyone who owns a helmet owns a bicycle

Explanation

The first sentence says bicycle owners are a subset of helmet owners, so no helmet owner can lack a bicycle. The second sentence merely confirms the subset is non-empty.

Question 40Higher order thinking and problem-solving

A farmer has 17 sheep. All but 9 run away. How many sheep remain?

  1. 17
  2. 0
  3. 8
  4. 9 Correct answer.

Explanation

The phrase 'all but 9' means every sheep except 9 left, so 9 sheep stay behind. The total of 17 is a distractor that invites subtracting 9 from it.

Question 41Reasoning

A train travels 180 km in 3 hours. At the same average speed, how far will it travel in 5 hours?

  1. 300 km Correct answer.
  2. 270 km
  3. 360 km
  4. 240 km

Explanation

The speed is 180 ÷ 3 = 60 km per hour. In 5 hours the train covers 60 × 5 = 300 km.

Question 42Reasoning

Find the next number in the sequence: 2, 6, 12, 20, 30, ...

  1. 36
  2. 40
  3. 44
  4. 42 Correct answer.

Explanation

The differences between consecutive terms are 4, 6, 8, 10, so the next difference is 12. Adding 12 to 30 gives 42.

Question 43Reasoning

All roses in the garden are red. Some red flowers in the garden are tulips. Which statement must be true?

  1. Some red flowers in the garden are roses. Correct answer.
  2. Every red flower in the garden is a rose.
  3. Some roses in the garden are tulips.
  4. All tulips in the garden are roses.

Explanation

Since all roses are red, every rose is a red flower, so some red flowers are roses. The tulip information does not force any link between tulips and roses.

Question 44Reasoning

Which word does not belong with the others?

  1. Iron
  2. Copper
  3. Granite Correct answer.
  4. Zinc

Explanation

Copper, iron and zinc are all metals, while granite is a rock. The odd one out is the non-metal.

Question 45Reasoning

If CAT is coded as 3-1-20, how is DOG coded using the same letter-to-position scheme?

  1. 4-14-7
  2. 4-15-6
  3. 4-15-7 Correct answer.
  4. 3-15-7

Explanation

Each letter is replaced by its position in the alphabet: D=4, O=15, G=7. So DOG becomes 4-15-7.

Question 46Reasoning

A square has a side length of 7 cm. What is its perimeter?

  1. 14 cm
  2. 49 cm
  3. 28 cm Correct answer.
  4. 21 cm

Explanation

A square has four equal sides, so the perimeter is 4 × 7 = 28 cm.

Question 47Reasoning

Book is to Reading as Fork is to ...

  1. Cooking
  2. Metal
  3. Kitchen
  4. Eating Correct answer.

Explanation

A book is the tool used for reading, just as a fork is the tool used for eating. The relationship is tool-to-action.

Question 48Reasoning

What is the next number: 3, 9, 27, 81, ...?

  1. 243 Correct answer.
  2. 108
  3. 324
  4. 162

Explanation

Each term is multiplied by 3, so the next term is 81 × 3 = 243.

Question 49Reasoning

Five friends sit in a row. Amy is to the left of Ben. Ben is to the left of Cara. Dan is to the right of Cara. Who must be to the left of Dan?

  1. Only Cara
  2. Only Amy and Ben
  3. Amy, Ben and Cara Correct answer.
  4. Only Ben

Explanation

The chain Amy < Ben < Cara < Dan places Amy, Ben and Cara all to the left of Dan. Therefore all three must be left of Dan.

Question 50Reasoning

A shirt is reduced by 20% and then the reduced price is reduced by a further 10%. What is the total percentage reduction from the original price?

  1. 27%
  2. 28% Correct answer.
  3. 30%
  4. 32%

Explanation

After 20% off, 80% remains. A further 10% off leaves 80% × 90% = 72% of the original, so the total reduction is 28%.