Sample Questions from Test 19

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

Mathematical Reasoning

Arlo has 27 stamps and Myra has 39 stamps. How many stamps must Myra give to Arlo so that he will have twice …

Question 1 · Multiple choice

Question

Arlo has 27 stamps and Myra has 39 stamps. How many stamps must Myra give to Arlo so that he will have twice as many stamps as she?

Options

A. $6$
B. $13$
C. $17$
D. $22$
E. $12$

Correct answer

C.

17

Explanation

Step 1: Set up the equation Let x = the number of stamps Myra gives to Arlo. After the transfer: Arlo has: 27 + x Myra has: 39 - x "Arlo will have twice as many as Myra": 27 + x = 2 \times (39 - x) Step 2: Solve 27 + x = 78 - 2x x + 2x = 78 - 27 3x = 51 x = 17 Step 3: Verify Person Before After giving 17 Arlo 2744 Myra 3922 Is 44 = 2 \times 22? Yes ✓ Answer: Myra must give 17 stamps to Arlo

Mathematical Reasoning

3/4 of Edward's money is equal to 1/3 of Janet's money. If Janet has \$35 more than Edward, how much money do…

Question 2 · Multiple choice

Question

3/4 of Edward's money is equal to 1/3 of Janet's money. If Janet has $35 more than Edward, how much money does Edward have?

Options

A. $$35$
B. $$28$
C. $$42$
D. $$21$
E. $$56$

Correct answer

B.

$28

Explanation

Step 1: Turn the fraction condition into a relationship between E and J "3/4 of Edward's money equals 1/3 of Janet's money": (3/4) × E = (1/3) × J Multiply both sides by 3: (9/4) × E = J So Janet has 9/4 times as much as Edward. Step 2: Use the difference condition "Janet has $35 more than Edward": J − E = 35 Substitute J = (9/4)E: (9/4)E − E = 35 Convert E to quarters: (9/4)E − (4/4)E = (5/4)E (5/4)E = 35 Step 3: Solve for E E = 35 × (4/5) = 35 × 4 ÷ 5 = 140 ÷ 5 = $28 Check: Edward = $28 Janet = (9/4) × 28 = $63 Difference: 63 − 28 = $35 ✓ Fraction check: (3/4) × 28 = 21 = (1/3) × 63 ✓ Answer: Edward has $28 OptionValueWhy it is wrongA$35The difference given — not Edward's amount. ✗B$28(5/4)E = 35 → E = 28. ✓C$42Solved for Janet's amount. ✗D$21Used (3/4) × 28 = 21 incorrectly as the answer. ✗E$56Multiplied instead of divided. ✗

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OC Mathematical Reasoning Practice Test 19 — 2027 NSW Opportunity Class Exam

Skills Covered in this Test

Sample Questions from Test 19

Core Competencies

Prepare with Precision

Option	Value	Why it is wrong
A	$35	The difference given — not Edward's amount. ✗
B	$28	(5/4)E = 35 → E = 28. ✓
C	$42	Solved for Janet's amount. ✗
D	$21	Used (3/4) × 28 = 21 incorrectly as the answer. ✗
E	$56	Multiplied instead of divided. ✗