Numerical Reasoning Test Practice Course: Percentages, percentage change and ratios

1. Question 1 of 18

   What is 15% of $240?

   • A$204
   • B$3.60
   • C$36
   • D$16
   Show answer

   Answer: C. $36

   15% = 0.15. 0.15 × 240 = $36.

2. Question 2 of 18

   Of 60 staff, 45 have finished their training. What percentage have finished?

   • A75%
   • B45%
   • C133%
   • D25%
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   Answer: A. 75%

   Part ÷ whole × 100: 45 ÷ 60 × 100 = 75%.

3. Question 3 of 18

   A product costs $80. The price goes up by 10%. What is the new price?

   • A$88
   • B$80.80
   • C$8
   • D$90
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   Answer: A. $88

   10% of $80 is $8. New price = 80 + 8 = $88. You can also multiply by 1.10.

4. Question 4 of 18

   Weekly orders went from 400 to 460. What is the percentage increase?

   • A60%
   • B115%
   • C13%
   • D15%
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   Answer: D. 15%

   Change ÷ starting value × 100: (460 − 400) ÷ 400 × 100 = 15%. Always divide by the starting (base) value.

5. Question 5 of 18

   Overtime fell from 120 hours to 90 hours. What is the percentage decrease?

   • A25%
   • B33.3%
   • C75%
   • D30%
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   Answer: A. 25%

   Decrease ÷ starting value × 100: 30 ÷ 120 × 100 = 25%. 33.3% comes from dividing by the new value.

6. Question 6 of 18

   A team has 12 supervisors and 48 other staff. What is the ratio of supervisors to other staff in its simplest form?

   • A12:60
   • B4:1
   • C1:4
   • D1:5
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   Answer: C. 1:4

   12:48. Divide both parts by 12 to get 1:4. Keep the order the question uses: supervisors first.

7. Question 7 of 18

   Part-time and full-time staff are in the ratio 3:5. There are 40 staff in total. How many are part-time?

   • A8
   • B24
   • C25
   • D15
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   Answer: D. 15

   3 + 5 = 8 parts. Each part = 40 ÷ 8 = 5 staff. Part-time = 3 × 5 = 15.

8. Question 8 of 18

   A $9,000 budget is shared between Team A and Team B in the ratio 2:1. How much does Team A get?

   • A$4,000
   • B$3,000
   • C$6,000
   • D$4,500
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   Answer: C. $6,000

   2 + 1 = 3 parts. One part = 9,000 ÷ 3 = $3,000. Team A gets 2 parts = $6,000.

9. Question 9 of 18

   The share of customers who were satisfied rose from 60% to 66%. By how many percentage points did it rise?

   • A6 percentage points
   • B10 percentage points
   • C66 percentage points
   • D1.1 percentage points
   Show answer

   Answer: A. 6 percentage points

   A change in percentage points is a simple subtraction: 66 − 60 = 6 percentage points.

10. Question 10 of 18

    The share of customers who were satisfied rose from 60% to 66%. What is the percentage increase in the satisfaction rate?

    • A6%
    • B10%
    • C9.1%
    • D66%
    Show answer

    Answer: B. 10%

    Percentage change = change ÷ starting value × 100 = 6 ÷ 60 × 100 = 10%. This is different from the 6-percentage-point rise.

11. Question 11 of 18

    After a 25% discount, a jacket costs $60. What was the price before the discount?

    • A$80
    • B$85
    • C$45
    • D$75
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    Answer: A. $80

    After a 25% discount you pay 75% of the price. Original = 60 ÷ 0.75 = $80. Adding 25% to $60 gives $75, which is wrong because 25% was taken from the original price.

12. Question 12 of 18

    A bill is $189.00 including 5% tax. What was the amount before tax?

    • A$180.00
    • B$179.55
    • C$198.45
    • D$184.00
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    Answer: A. $180.00

    The bill is 105% of the pre-tax amount. Pre-tax = 189 ÷ 1.05 = $180.00. Taking 5% off $189 gives $179.55, which is wrong.

13. Question 13 of 18

    Sales were $5,000 in February. They rose 10% in March, then fell 10% in April. What were April sales?

    • A$4,500
    • B$4,950
    • C$5,000
    • D$5,050
    Show answer

    Answer: B. $4,950

    March = 5,000 × 1.10 = $5,500. April = 5,500 × 0.90 = $4,950. The 10% fall is taken from the bigger March figure, so you do not get back to $5,000.

14. Question 14 of 18

    The table shows new customers by region last month. What percentage of all new customers came from the South region?

    Region	New customers
    North	120
    South	180
    East	150
    West	50

    • A56%
    • B36%
    • C64%
    • D18%
    Show answer

    Answer: B. 36%

    Total = 500. South share = 180 ÷ 500 × 100 = 36%.

15. Question 15 of 18

    A cleaning product is mixed 1 part concentrate to 24 parts water. How much concentrate is in 5 litres of mixed solution?

    • A120 mL
    • B2,000 mL
    • C200 mL
    • D208 mL
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    Answer: C. 200 mL

    1 + 24 = 25 parts in total. 5 L = 5,000 mL. One part = 5,000 ÷ 25 = 200 mL of concentrate. Dividing by 24 forgets the concentrate itself is a part.

16. Question 16 of 18

    Which store had the largest percentage increase in sales from last year to this year?

    Store	Sales last year	Sales this year
    Store 1	$52,000	$57,200
    Store 2	$80,000	$86,400
    Store 3	$35,000	$38,850
    Store 4	$64,000	$69,760

    • AStore 3
    • BStore 4
    • CStore 1
    • DStore 2
    Show answer

    Answer: A. Store 3

    Percentage increases: Store 1 10.0%, Store 2 8.0%, Store 3 11.0%, Store 4 9.0%. Store 3 grew fastest, even though Store 2 had the biggest dollar increase.

17. Question 17 of 18

    40% of staff are part-time. Of the part-time staff, 25% work weekends. What percentage of ALL staff are part-time weekend workers?

    • A65%
    • B10%
    • C25%
    • D15%
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    Answer: B. 10%

    Take a percentage of a percentage by multiplying: 0.40 × 0.25 = 0.10, which is 10% of all staff.

18. Question 18 of 18

    Shop A grew from $200,000 to $220,000 (10%). Shop B grew from $800,000 to $840,000 (5%). What was the percentage growth of the two shops combined?

    • A15.0%
    • B6.0%
    • C5.7%
    • D7.5%
    Show answer

    Answer: B. 6.0%

    Combine the totals: from $1,000,000 to $1,060,000, a rise of $60,000. 60,000 ÷ 1,000,000 × 100 = 6.0%. A simple average of 10% and 5% ignores that Shop B is much bigger.

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