**Solutions to The Department of WA Gifted and Talented (ASET) Quantitative Reasoning Sample Test**

Yes, we hear you parents. While the Education Department has provided the answers to their Quantitative Reasoning Sample Test, solutions are not provided. We appreciate that some of the questions are challenging, even for parents.

We have worked out the solutions to each sample question to the Quantitative Reasoning Sample Test, which is the hardest test among all the papers, as attached.

Here is the link to the sample test from the Education Department’s website if you have not already downloaded it for your child to practise https://www.education.wa.edu.au/dl/rn3oojz

Question | Answer | Explanation |

1 | B | We know that three large paper clips and one small paper clip is 10g or: L + L + L + S = 10. —(1) And if we take one large paper clip away we have 7.2 g: L + L + S = 7.2 —(2) This means that two large paper clips and one small paper clip weighs 7.2. Substituting (2) into (1): L + 7.2 = 10 So, a large paper clip is 10 – 7.2 = 2.8 Using this information two large paper clips are: 2.8 x 2 = 5.6 So, a small paper clip is: 7.2 – 5.6 = 1.6g. |

2 | A | For a pack of 10 cards, each card costs: 6 10 = 0.6 or 60 cents For a pack of 12 cards: 6 12 = 0.5 or 50 cents. So, the difference in price per card is 60 – 50 = 10 cents. |

3 | D | The first thing we will do is find out how many students prefer each food in each class. For students studying Italian: There are 8 students in total. Looking at the graph we see ¼ prefer sushi and ¾ or the remaining students prefer pizza. So, 8 4 = 2 prefer sushi Therefore 8 – 2 = 6 prefer pizza. For students studying Japanese: There are 16 students in total where ¼ of them prefer pizza and the remaining ¾ prefer sushi. So, 16 4 = 4 students prefer pizza. Therefore 16 – 4 = 12 students prefer sushi. Adding up the number of students in the class: 8 + 16 = 24. Number that prefer sushi = 2 + 12 = 14 = 14/24 = 7/12 Number of students that prefer pizza = 6 + 4 = 10 = 10/24 = 5/12 Now we know that the fraction of students that prefer sushi is higher than that of those that prefer pizza. Since the difference between the fractions is not very large the answer cannot be A so it must be D. |

4 | A | If Ms Biatza buys pizza for half the class and sushi for half the class this means that there is a share of pizza for 12 people and a share of sushi for 12 people. This isn’t a problem for those that prefer pizza since there are only 10 people who prefer pizza. However, we know that 14 people prefer sushi. This means that 14-12 = 2 people will not get to eat the food they prefer. |

5 | B | With the information, we are given we know that for a full rotation of A, B’s numbers change by 7 in the clockwise direction and C’s numbers change by 7 in the anticlockwise direction. If 3 full turns are made this means that gears B and C will move 7 x 3 = 21 places. For gear B, the largest number is 10 this means that if the gear moves 10 times for a full rotation. If it moves 21 times: 10 + 10 + 1 = 21, we get two full rotations and one more turn. This means that the number shown is 1+ 1 = 2. For gear C, the largest number is 9, so: 9 + 9 + 3 = 21. We get two full rotations and 3 more turns so the number shown is = 1 + 3 = 4. |

6 | B | For gear C to make a full rotation the gear must turn 9 times. If gear A turns 9 times, the largest number is 7 so 7 + 2 = 9. So, gear A makes one full rotation and 2 more turns: 1 + 2 =3. Hence, the number shown is 3. |

7 | A | 10 full turns of gear A means the gear turns 7 x 10 = 70 times. For gear B this is just 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70 or 70 10 = 7 full rotations this means the number shown is simply 1. |

8 | D | All we need to do here is find the lowest common multiple of the number times each gear has to turn to make a full rotation. Which is: 7,10 and 9 respectively. Using elimination, we should find the answer which can be divided by all of these numbers. 7 cannot be divided by 10 or 9 26 cannot be divided by any of the numbers 260 cannot be divided by 7 or 9. 630 can be divided by all the numbers. 630 10 = 63, 630 7 = 90, 630 9 = 70. Hence, the answer is D. |

9 | D | Here we simple need to go through each option and see whether the animals can be displayed together. It is important to check the answer in 3 combinations, for instance if animals A, B and C are displayed together: the combinations we have are: A &B, B & C, and A & C. All of these combinations must be possible for the answer to be true. Option A: yellow and blue cannot be displayed together Option B: red and brown cannot be displayed together Option C: green and red cannot be displayed together Option D: the animals can be displayed together. Hence, the answer is D. |

10 | B | What we can do is use the answer to form the operations and whole numbers that we use. The # represents and operation a whole number then a different operation after it, for example: x 3 – For our equation: 3 # (2 # 1) the answers we are given are relatively small, so our whole number should also be. Trying numbers 1, 2 and 3 should be sufficient. The operation combinations we can have are 12 in total: + and then – x and then – + and then x x and then + and then x and then + – and then + and then – – and then x and then + – and then and then x The smartest thing to do here is to eliminate the options that will not give us whole numbers and then make an intelligent guess from the remaining options. In this case we should steer clear of any division since the numbers are quite small. After trial and error. We can find a combination that fulfils the answer. If # = x 2 – Then 3 x 2 – (2 x 2 – 1) = 6 – 3 = 3. |

11 | C | We discovered that # = x 2 – So, substituting this into the equation: (4 x 2 – 1) x 2 – (5 x 2 – ?) = 9 (7) x 2 – (10 -?) = 9 = 14 – (10 – ?), 14 – 5 =10. Hence, ? = 5. |

12 | A | We know that a ¼ of the tracks he bought from Buytunes are EDM this means that the 6 tracks are a quarter of the tracks bought from Buytunes. So, tracks bought from Buytunes = 6 x 4 = 24. Now, we also know that ½ of his purchases come from Buytunes. This means that ½ of his total tracks or 24 tracks came from Buytunes. If this is the case this means the total number of tracks he bought is 24 x 2 = 48 tracks. If a 1/3 of them came from Generic Trax: 48 3 = 16. Now to find the number of K-Pop tracks. 1/8 of the tracks from Generic Trax are K-Pop so 16 8 = 2. |

13 | D | If 24 tracks were downloaded from Spotibuy, since 1/6 of the tracks he bought are from Spotibuy this means that there are 24 x 6 = 144 tracks in total. Half of those were Buytunes: 144 2 = 72. |

14 | A | Gold is the only metal that does not show a positive value when compared to another metal. The table tells us that Copper is 44 units more reactive than Gold and gold is 71 units less reactive than lead. Hence, the answer is A. |

15 | B | Lead is 27 units more reactive than Copper and 111 units less reactive than Magnesium. Since Aluminium is 86 units less reactive than Magnesium, it follows that: Magnesium> Aluminium > Lead > Copper |

16 | D | Gold is 71 units less reactive than Lead and Lead is 111 units less reactive than Magnesium. Hence, Gold is 71 + 111 = 182 units less reactive than Magnesium or -182. |

17 | B | For this question, we can look at the number of people whose emotions were correctly identified Anger: 68% Sadness: 65% Happiness: 70% Neutral: 81% The smallest here is sadness, this means that sadness was the emotion that had the least amount of people that were correctly identified. |

18 | A | Looking at the first two tests and the options given: Mistaking Angry Face for Sad Face: Test 2 = 18% Sad Face for Angry Face Test 2 = 6% Angry Voice for Sad Voice Test 1 = 5% Sad Voice for Angry Voice Test 1 = 7% Hence, it was the most likely to mistaken an angry face for a sad face. |

19 | C | Test 3 Test 2 Anger: 94% 79% Lower Sadness: 79% 81% Higher Happiness: 90% 100% Higher Neutral: 92% 81% Lower Hence, 2 emotions were better classified by face than by voice. |

20 | D | We can see that the dots that have been changed are the bottom right, middle right and bottom middle dots. This means only those colours have been flipped, hence for this to be possible the bottom right dot must have been selected as the x. |

21 | B | All the dots affect the middle dot except those in the corners which is 4. Hence the number of times that the middle dot is turned = 9 – 4 = 5 times |

22 | D | The dots appear like so: 1^{st}, 2^{nd} and 3^{rd}. |

23 | B | People who watch SuperChef in State 2: 4 x 0.5 = 2 million People who watch SuperChef in State 6: 5 x 0.2 = 1 million Hence, 1 million more people watch SuperChef in State 2 than State 6. |

24 | B | For each state: State 1 = 5 x 0.1 = 0.5 million State 2 = 4 x 0.5 = 2 million State 3 = 10 x 0.1 = 1 million State 4 = 20 x 0.1 = 2 million State 5 = 6 x 0.2 = 1.2 million State 6 = 5 x 0.2 = 1 million In total = 0.5 + 2 + 1 + 2 + 1.2 + 1 = 7.7 million |

25 | B | In State 6: 5 – 1 = 4 million people do not watch SuperChef. This is double of the number of people who do watch SuperChef in State 4 and 2. Hence, the answer is B. |

26 | D | Bobby finds 5 white flowers within a 1 x 1 = 1m^{2} area.Since the entirety of the lawn is a 10 x 13 = 130m This means there is an estimated 130 x 5 = 650 white flowers on the whole lawn. |

27 | C | If she estimates there are 132 white flowers this means that the area of the lawn is 132 6 = 22m^{2}All we have to do now is find the dimensions that will equate to this area from the options given. Option A = 5 x 2 = 10 Option B = 5 x 4 = 20 Option C = 11 x 2 = 22 Hence, C is the answer. |

28 | B | First, we will find the area of the lawn. We can split the lawn into two areas and find them separately. Finding A = 4 x 2 = 8 Finding B = 6 x 4 = 24 Total area = 8 + 24 = 32m
So total estimate is 3 x 32 = 96 yellow flowers. |

29 | C | By using the diagram in the question, we can rank the teams from strongest to weakest. Chuditches > Malas > Dibblers > Numbats > Woylies > Quokkas Hence, the result that would not occur is C. The Woylies cannot defeat the Dibblers. |

30 | A | If we add the Boodies into our line-up: Boodies > Numbats > Woylies > Quokkas We can see that the Boodies are certain to defeat the Woylies. |

31 | C | We will look at the times where the image in the photo was incorrectly interpreted by the machine, i.e when the photo shows a car, but the computer does not report it and the photo does not show a car and the computer mistaken reports one. Times the computer was incorrect: 22 + 12 = 34 |

32 | A | For Test 1 Accuracy in reporting photos without cars=42/42+12 = 42/54 = 7/9 = 0.78 Test 2 Accuracy in reporting photos without cars=46/46+22 = 46/68 = 23/34 = 0.68 Test 3 Accuracy in reporting photos without cars=104/104+24 = 104/128 = 13/16 = 0.81 Hence, Test 2 is the least accurate. |

33 | C | Rose has a 4kg cat and 4kg small dog. For the cat: 1 + (1.5 x 4) = 1 + 6 = 7kg For the small dog: 2 + (2 x 4) = 2 + 8 = 10 kg. |

34 | B | A 5kg small dog would need: 2 + (2 x 5) = 2 + 10 = 12 pills per day Hence, 60 pills would last: 60 12 = 5 days. |

35 | A | We can use trial and error to see which animal fits the total amount given. For a cat: 1 + (1.5 x 6) = 1 + 9 = 10kg. Hence, the answer is A. |