New Syllabus Mathematical Reasoning

Summary of Changes

The mathematical part of the earlier exam has been replaced with a new section called Mathematical Reasoning. In the earlier selective exams there were purely mathematical questions and general ability questions requiring little interpretation of the problem. This section now requires English skills in addition to mathematical skills. We have created new content which reflects the new type of questions incorporating English with Mathematics. To know more about the changes we have made click the link below.

Time Problems

Q. Tom leaves Sydney on a 2.00 P.M. flight destined for Perth. The flight duration is 4 hours and 55 minutes. The flight lands in Perth 15 minutes late. Sydney time is 3 hours ahead of Perth time. What is the time the flight lands in Perth?

  1. 15:55
  2. 14:55
  3. 15:10
  4. 16:10


Answer. D


The flight duration is 5 hours and 10 minutes. So, it lands in Perth at 7.10 P.M. or 19.10 in the twenty-hour format Sydney time. So, the Perth time 16.10 A.M.




Q. A chocolate bar is shown below

. Andrew ate 8 small pieces. Betty ate half of A. Cathy 1/3 of the remaining bars. Danny ate the remaining pieces. Which of the following statements are correct?

  1. Betty and Cathy ate the equal number of small pieces.
  2. Andrew and Danny both ate equal number of small pieces.
  3. Andrew ate the equal number of small pieces as Betty and Cathy together.
  4. Cathy ate half the number of pieces as Danny.
  5. Danny ate eight small pieces.

Which of above statements is correct?

           A. Statement 1 only.

          B. Statement 1 and statement 2 only.

        C. Statement 1, 2, and 3 only.

        D. Statement 1, 2, 3 and 4 only­­­­­­­­­­­

        E. All statements are correct


Answer. E


There are 4 small pieces in each row and there are six rows. So total small pieces are 24. Andrew ate 8 small pieces or 8/24th   1/3rd or 2/6th of the chocolate. This means that Betty ate 4 pieces or 4/24th or 1/6th of the chocolate. Together Andrew and Betty ate 2/6th plus 1/6th of the chocolate. So, they ate ½ of the chocolate or 12 pieces. So Cathy ate 1/3rd of 12 remaining pieces or 4 pieces or 4/24 or 1/6  of the chocolate. The remaining 8 pieces were eaten by Danny. The information is tabulated below.

Andrew Betty Cathy Danny
2/6 1/6 1/6 2/6
8 small pieces 4 small pieces 4 small pieces 8 small pieces.

So, the correct answer is E.


Q3. Consider the following events.

Jack throws a dice and gets a 3.

Sam spins a spinner numbered one to eight and also gets a 3.

Tom tosses a coin and gets a head.

Danny withdraws a blue ball from a bag containing 4 blue and 6 red balls.

Jenny spins a spinner numbered one to five and gets a five.

Which of the following statements is correct?

Which of the following sequences correctly represents their probabilities in ascending order?

  1. Jack, Sam, Tom, Danny, Jenny
  2. Jenny, Jack, Sam, Danny, Tom
  3. Jack, Jenny, Sam, Danny, Tom
  4. Jenny, Sam, Jack, Danny, Tom
  5. Jenny, Jack, Sam, Tom, Danny


 Answer B






1/3= 33.33%


1/2= 50%

4/10=2/5= 40%




Bar Diagram

Q4. The runs scored by a batsmen in 7 innings are shown below

Statement 1. The median score is 33.
Statement 2. The difference between the two lowest numbers is less than the difference between the two highest numbers.
Statement 3. The minimum difference between two scores is 5.
Statement 4. The difference between the highest score and the median score is 25.
Statement 5. The difference between the two numbers adjacent to the median is 35.

Which of the following answers is correct?

A. None of the statements is true.
B. All statements are true.
C. All statements except statement 1 are correct.
D. All statements except 3 are wrong.
E. All statements except 4 statement 5 are wrong.

Line Diagram

Q. The following table shows the temperature in Celsius on 14th Dec 2020


Statement 1- The temperature at 10 A.M. and 7 P.M differ by 1 degree Celsius.

Statement 2. The median temperature is 40 degrees Celsius.

Statement 3. The mean temperature during the day is approximately 25 degree Celsius.

Statement 4. The difference between the highest and lowest temperature is 25 degree Celsius.

Statement 5. It was a hot day.

Which of the following statements is correct?

          A. All statements are correct.

         B. None of the statements is correct.

        C. Statement 1, 2, 4 and 5 are correct.

       D. Statement 1, 2, 3 and 4 are correct

      E. Statement 2, 3, 4 and 5 are correct


      Answer. A


All statements are correct. So, the answer is A. The temperatures sorted in the ascending order are given below.

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