Year selective Numerical Reasoning | Victorian Curriculum 2.0
Quantitative word problems
Topic 03 | Numerical reasoning | Answer key

Each answer shows the one-unit value or one-part value first, then the scaling.

Timed drill

    1. (b) $12. One apple costs 4÷5=804 \div 5 = 80 cents. Fifteen apples: 15×0.80=1215 \times 0.80 = 12 dollars.
    2. (c) 300 g. One person =200÷4=50= 200 \div 4 = 50 g. Six people =6×50=300= 6 \times 50 = 300 g.
    3. (d) $50. Total parts =3+5=8= 3 + 5 = 8. One part =80÷8=10= 80 \div 8 = 10 dollars. Second friend =5×10=50= 5 \times 10 = 50 dollars.
    4. (c) 300 km. Speed =120÷2=60= 120 \div 2 = 60 km/h. Distance =5×60=300= 5 \times 60 = 300 km.
    5. (c) 6. 20%=1520\% = \tfrac{1}{5}. 15×30=6\tfrac{1}{5} \times 30 = 6.
    6. (c) $45. 25%=1425\% = \tfrac{1}{4}. Discount =15= 15 dollars. Sale price =60−15=45= 60 - 15 = 45 dollars.
    7. (b) 10 min. Each tap fills 130\tfrac{1}{30} per min; three taps fill 330=110\tfrac{3}{30} = \tfrac{1}{10} per min. Time =10= 10 min.
    8. (b) 4. Worker-days =8×6=48= 8 \times 6 = 48. 48÷12=448 \div 12 = 4 days.
    9. (c) 9. Total parts =1+2+2=5= 1 + 2 + 2 = 5. One part =45÷5=9= 45 \div 5 = 9. Smallest share =1×9=9= 1 \times 9 = 9.
    10. (d) 60 km. 4545 min =34= \tfrac{3}{4} hour. Distance =80×34=60= 80 \times \tfrac{3}{4} = 60 km.
    11. (c) 48 L. 2424 hours ×2\times 2 L/hour =48= 48 L.
    12. (b) $55. 10%10\% of 5050 is 55 dollars. New price =55= 55 dollars.
    13. (c) 25. Ratio 2:32 : 3, so 22 parts =10= 10 boys, 11 part =5= 5. Total 55 parts =25= 25.
    14. (c) 17. 100÷6=16100 \div 6 = 16 remainder 44. The last 44 books still need a box, so 1717 boxes.
    15. (d) 6. Flour doubles, so water doubles too: 3×2=63 \times 2 = 6 cups.
    16. (c) $90. 12×7.5=9012 \times 7.5 = 90 dollars.
    17. (d) 48. One pizza =16= 16 slices. 33 pizzas =48= 48 slices.
    18. (b) 16. If 60%60\% are girls, 40%40\% are boys. 40%40\% of 40=1640 = 16.
    19. (a) $3.50. 10×0.35=3.5010 \times 0.35 = 3.50 dollars.
    20. (c) $20. Total parts =1+2+3=6= 1 + 2 + 3 = 6. One part =60÷6=10= 60 \div 6 = 10 dollars. Middle share =2×10=20= 2 \times 10 = 20 dollars.

Challenge

    1. (d) 60 min. Net drain rate =120−130=360−260=160= \tfrac{1}{20} - \tfrac{1}{30} = \tfrac{3}{60} - \tfrac{2}{60} = \tfrac{1}{60} per minute. So 6060 minutes to empty the full tank.
    2. (b) 6 days. Worker-days =4×9=36= 4 \times 9 = 36. 36÷6=636 \div 6 = 6 days.
    3. (c) 25%25\%. Profit =5= 5 dollars. Percent profit =5/20=14=25%= 5 / 20 = \tfrac{1}{4} = 25\%.
    4. (b) 14. Ratio 2:52 : 5, so difference == 33 parts =21= 21, giving 11 part =7= 7. Cats =2×7=14= 2 \times 7 = 14.
    5. (b) 6. 1.51.5 L =1500= 1500 mL. 1500÷250=61500 \div 250 = 6 full cups.
    6. (b) $72. After first discount: 120×0.75=90120 \times 0.75 = 90 dollars. After second: 90×0.80=7290 \times 0.80 = 72 dollars.
    7. (b) 2.5 hr. Opposite directions, so combined speed =40+60=100= 40 + 60 = 100 km/h. Time =250÷100=2.5= 250 \div 100 = 2.5 hours.
    8. (d) 19:1619 : 16. Ratio 3:43 : 4 of 2828 marbles gives 1212 red, 1616 blue. After adding 77 red: 1919 red, 1616 blue.
Year selective Numerical Reasoning study companion | Answer key