Sample Questions from Test 16

The first two questions of this mock test (same order and wording as the timed exam).

Mathematical Reasoning

Two apples weigh the same as five mandarins.

Question 1 · Multiple choice

Question

Two apples weigh the same as five mandarins. Bag X: 10 apples and 10 mandarins Bag Y: 4 apples and 25 mandarins Bag Z: 14 apples and 5 mandarins Which statement is correct ?

Options

A. $All three bags weigh the same.$
B. $X and Y weigh the same; Z is different.$
C. $X and Z weigh the same; Y is different.$
D. $Y and Z weigh the same; X is different.$
E. $All three bags have different masses.$

Correct answer

B.

X and Y weigh the same; Z is different.

Explanation

Step 1: Create a common unit We are told: 2 apples = 5 mandarins Let 1 mandarin = 2 units (an arbitrary unit of weight). Then 5 mandarins = 5 \times 2 = 10 units. Since 2 apples = 5 mandarins = 10 units: 1 apple = 10 \div 2 = 5 units Step 2: Calculate the weight of each bag Bag X: 10 apples + 10 mandarins = 10 \times 5 + 10 \times 2 = 50 + 20 = 70 units Bag Y: 4 apples + 25 mandarins = 4 \times 5 + 25 \times 2 = 20 + 50 = 70 units Bag Z: 14 apples + 5 mandarins = 14 \times 5 + 5 \times 2 = 70 + 10 = 80 units Step 3: Compare Bag Weight X 70 units Y 70 units Z 80 units X and Y are equal; Z is heavier. Answer: X and Y weigh the same; Z is different

Mathematical Reasoning

A mother is currently 5 times as old as her daughter. Four years later, the mother will be 4 times as old as …

Question 2 · Multiple choice

Question

A mother is currently 5 times as old as her daughter. Four years later, the mother will be 4 times as old as her daughter. How old is the daughter now?

Options

A. $10$
B. $11$
C. $12$
D. $13$
E. $14$

Correct answer

C.

12

Explanation

Step 1: Write expressions for both ages now Let daughter's age now = D Mother's age now = 5D (5 times the daughter) Step 2: Write the equation for 4 years' time In 4 years: Daughter = D + 4 Mother = 5D + 4 "Mother will be 4 times daughter's age": 5D + 4 = 4 \times (D + 4) 5D + 4 = 4D + 16 D = 12 Step 3: Find mother's age now Mother = 5 \times 12 = 60 years old Check: In 4 years: daughter = 16, mother = 64. Is 64 = 4 \times 16? Yes ✓ Answer: The daughter is 12 years old now

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OC Mathematical Reasoning Practice Test 16 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 16

Core Competencies

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