Sample Questions from Test 12

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

Mathematical Reasoning

Town A and Town B are 900 kilometres apart. A car that travels at 80 kilometres per hour leaves Town A for To…

Question 1 · Multiple choice

Question

Town A and Town B are 900 kilometres apart. A car that travels at 80 kilometres per hour leaves Town A for Town B. At the same time, another car leaves Town B for Town A at 70 kilometres per hour. When will the two cars meet?

Options

A. $6 hours$
B. $5 hours$
C. $4.5 hours$
D. $7 hours$
E. $8 hours$

Correct answer

A.

6 hours

Explanation

Step 1: Understand the situation The two cars leave at the same time and drive toward each other. Together, they are closing the 900 km gap between them. Town A ────────────────────────────── Town B Car 1 ──▶ 80 km/h 70 km/h ◀── Car 2 They meet somewhere here! Step 2: Find the combined closing speed Since both cars move toward each other, their speeds add together: Combined speed = 80 + 70 = 150 km/h Think of it this way: every hour, Car 1 covers 80 km and Car 2 covers 70 km, so together they cover 150 km of the 900 km gap. Step 3: Find the time until they meet Time = Distance \div Speed = 900 \div 150 = 6 hours Check: After 6 hours, Car 1 has travelled 80\times6 = 480 km, Car 2 has travelled 70\times6 = 420 km. Total = 480 + 420 = 900 km ✓ Answer: They meet after 6 hours Option Value Why it is wrong A 6 hours 900 \div 150 = 6. ✓ B 5 hours Used only one car's speed. ✗ C 4.5 hours Arithmetic error. ✗ D 7 hours Used 900 \div 80 + something incorrectly. ✗ E 8 hours Used 900 \div 80 alone (too slow). ✗

Mathematical Reasoning

A deck of 52 cards are printed with hearts, spades, diamonds and clubs. At least how many of these cards must…

Question 2 · Multiple choice

Question

A deck of 52 cards are printed with hearts, spades, diamonds and clubs. At least how many of these cards must a player draw in order to get 4 cards of the same pattern?

Options

A. $12$
B. $13$
C. $14$
D. $16$
E. $15$

Correct answer

B.

13

Explanation

Step 1: Understand the problem There are 4 suits (patterns): hearts ♥, spades ♠, diamonds ♦, clubs ♣. The question asks: what is the minimum number of cards needed to guarantee getting 4 cards of the same suit? Step 2: Think about the worst case Imagine the unluckiest possible draws — cards keep alternating between suits to delay getting 4 of the same. The worst case before getting 4 of any suit is having exactly 3 of each suit : 3 hearts + 3 spades + 3 diamonds + 3 clubs = 12 cards drawn, still no 4 of the same suit Step 3: The next card guarantees success No matter which suit the 13th card is, it joins a suit that already has 3 cards, making 4 of the same suit . Minimum cards = 3 \times 4 + 1 = 13 Answer: 13 cards Option Value Why it is wrong A 12 This is the worst case without success — the 12th card may not complete 4. ✗ B 13 3 \times 4 + 1 = 13 guarantees 4 of the same suit. ✓ C 14 One more than needed. ✗ D 16 Used 4 \times 4 = 16, incorrect reasoning. ✗ E 15 Arithmetic error. ✗

Prepare with Precision

Sharpen accuracy on multi-step and diagram-based items.
Get comfortable with the Janison-style interface.
Identify topics to revisit before exam day.

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Mathematical Reasoning Mock Test 12: 2027 NSW Selective Format

Skills Covered in this Test

Sample Questions from Test 12

Core Competencies

Prepare with Precision

Option	Value	Why it is wrong
A	6 hours	900 ÷ 150 = 6. ✓
B	5 hours	Used only one car's speed. ✗
C	4.5 hours	Arithmetic error. ✗
D	7 hours	Used 900 ÷ 80 + something incorrectly. ✗
E	8 hours	Used 900 ÷ 80 alone (too slow). ✗

Option	Value	Why it is wrong
A	12	This is the worst case without success — the 12th card may not complete 4. ✗
B	13	3 × 4 + 1 = 13 guarantees 4 of the same suit. ✓
C	14	One more than needed. ✗
D	16	Used 4 × 4 = 16, incorrect reasoning. ✗
E	15	Arithmetic error. ✗