OC Mathematical Reasoning Practice Test 7 — 2027 NSW Opportunity Class Exam

Strengthen problem solving, algebra, percentages, ratios, speed and distance, and geometry with this 35-question OC Mathematical Reasoning practice test. Matched to the 2027 NSW Opportunity Class Placement Test format and timed for real exam conditions.

Duration

40 Minutes

Format

2027 NSW Format

Questions

35 multiple-choice

Level

NSW OC Placement Test Level

Mathematical Reasoning

String A is 3/4 the length of string B. String C is 80% the length of string A. What is the ratio of the leng…

Question 1 · Multiple choice

Question

String A is 3/4 the length of string B. String C is 80% the length of string A. What is the ratio of the length of string A to string B to string C?

Options

A. $3 : 4 : 12$
B. $15 : 20 : 12$
C. $12 : 15 : 20$
D. $20 : 15 : 12$
E. $3 : 5 : 4$

Correct answer

15 : 20 : 12

Explanation

Step 1: Choose a convenient length for string B Let B = 20 units (divisible by 4 and 5 for clean calculations). Step 2: Find A A = 3/4 \times B = 3/4 \times 20 = 15 units Step 3: Find C C = 80% \times A = 0.8 \times 15 = 12 units Step 4: Write the ratio A : B : C = 15 : 20 : 12 Check if they can be simplified: GCD(15, 20, 12) = 1. Already in simplest form. A: ███████████████ 15 units B: ████████████████████ 20 units C: ████████████ 12 units Answer: A : B : C = 15 : 20 : 12

Mathematical Reasoning

A car travelled 7 hours from place A to place B. Its average speed was a kilometres per hour. For the first 4…

Question 2 · Multiple choice

Question

A car travelled 7 hours from place A to place B. Its average speed was a kilometres per hour. For the first 4 hours, it travelled b kilometres. Then for the next 3 hours its average speed was how many kilometres per hour?

Options

A. $(a - b) \div 3$
B. $(a - 4b) \div 3$
C. $(7a - 4b) \div 3$
D. $(7a - b) \div 3$
E. $(7a + b) \div 3$

Correct answer

(7a - b) \div 3

Explanation

Step 1: Find the total distance from A to B The car travels for 7 hours at an average speed of a km/h. Total distance = speed \times time = a \times 7 = 7a km Step 2: Find the remaining distance In the first 4 hours, the car covers b km . Remaining distance = Total distance - Distance already covered = 7a - b km Step 3: Find the average speed for the last 3 hours The remaining distance of (7a - b) km is covered in 3 hours . Speed = Distance \div Time = (7a - b) \div 3 Answer: (7a - b) \div 3 km/h Option Expression Why it is wrong A (a-b)\div3 Used a instead of 7a for total distance. ✗ B (a-4b)\div3 Mixed up a and 4b incorrectly. ✗ C (7a-4b)\div3 Multiplied b by 4 — b already covers first 4 hours. ✗ D (7a-b)\div3 7a-b divided by 3 hours. ✓ E (7a+b)\div3 Added first-leg instead of subtracting. ✗

OC Mathematical Reasoning Practice Test 7 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 7

Core Competencies

Prepare with Precision

Option	Expression	Why it is wrong
A	(a−b)÷3	Used a instead of 7a for total distance. ✗
B	(a−4b)÷3	Mixed up a and 4b incorrectly. ✗
C	(7a−4b)÷3	Multiplied b by 4 — b already covers first 4 hours. ✗
D	(7a−b)÷3	7a−b divided by 3 hours. ✓
E	(7a+b)÷3	Added first-leg instead of subtracting. ✗