Proportional Quantities Questions - CCAT Test Prep

This type of question tests your understanding of proportional relationships and how to scale quantities up or down based on a given ratio. In this example, the problem asks how many pounds of timber are needed if a specific amount is used to produce a certain number of beds. By breaking down the unit requirement, you can determine the total amount needed when scaling up the production.

proportional-quantities

How to Calculate Proportional Quantities?

Question 1 - Proportional Calculation

A factory requires 100 pounds of timber to produce 12 beds. At that rate, how many pounds of timber will it require to produce 300 beds?

  • A) 2100
  • B) 2500
  • C) 2800
  • D) 3000
  • E) 3200

Step-by-Step Mental Solution:

Calculate the Amount of Timber Needed for 1 Bed

  • 100 pounds are needed for 12 beds.
  • To determine how many pounds are needed for 1 bed:
Timber_per_bed 
     = 100 pounds / 12 beds 
     ≈ 8.33 pounds per bed

Calculate the Timber Needed for 300 Beds

  • Multiply the timber per bed by 300:
Total_timber 
    = 8.33 pounds per bed × 300 beds 
    ≈ 2500 pounds

Answer: 2500

Question 2 - Doubling the Production

If a factory uses 50 pounds of metal to produce 10 chairs, how many pounds of metal are required to produce 40 chairs?

  • A) 100
  • B) 150
  • C) 200
  • D) 250
  • E) 300

Step-by-Step Mental Solution:

Calculate Metal Required per Chair:

Metal_per_chair 
	= 50 pounds / 10 chairs 
	= 5 pounds per chair

Calculate Metal Needed for 40 Chairs:

Total_metal 
	= 5 pounds per chair × 40 chairs 
	= 200 pounds

Answer: 200

Question 3 - Scaling Up Materials

A company uses 120 pounds of plastic to make 15 toys. How much plastic is needed to produce 90 toys?

  • A) 600
  • B) 720
  • C) 840
  • D) 900
  • E) 960

Step-by-Step Mental Solution:

Calculate Plastic Required per Toy

Plastic_per_toy 
	= 120 pounds / 15 toys 
	= 8 pounds per toy

Calculate Plastic Needed for 90 Toys

Total_plastic 
	= 8 pounds per toy × 90 toys 
	= 720 pounds

Answer: 720

How to Solve These Questions in Your Head

  1. Find the Unit Value: Start by calculating how much material is needed for a single unit (e.g., how much timber per bed).
  2. Multiply by the Desired Number of Units: Once you have the unit value, multiply it by the desired number of units to get the total requirement.
  3. Keep the Math Simple: Try breaking numbers into manageable parts or rounding to make calculations easier, then adjust if needed.

By using these steps, you can easily calculate proportional relationships, making it possible to solve such problems quickly in your head or with minimal note-taking.

20 Practice Questions

  1. A car factory needs 80 gallons of paint to produce 16 cars. How many gallons are needed for 48 cars?
  • A) 160
  • B) 200
  • C) 220
  • D) 240
  • E) 300
  1. A bakery uses 12 cups of flour to make 24 muffins. How many cups are needed to make 96 muffins?
  • A) 36
  • B) 40
  • C) 42
  • D) 48
  • E) 50
  1. If 6 pounds of material are used to make 5 shirts, how many pounds are needed to make 25 shirts?
  • A) 24
  • B) 26
  • C) 28
  • D) 30
  • E) 32
  1. A landscaper needs 150 pounds of soil for 30 square meters of garden. How much soil is needed for 90 square meters?
  • A) 400
  • B) 425
  • C) 450
  • D) 475
  • E) 500
  1. A builder requires 500 bricks to construct 5 walls. How many bricks are needed to construct 20 walls?
  • A) 1800
  • B) 1900
  • C) 2000
  • D) 2100
  • E) 2200
  1. A chef uses 9 liters of broth to make 3 pots of soup. How many liters are required to make 12 pots?
  • A) 24
  • B) 30
  • C) 36
  • D) 42
  • E) 48
  1. A printer uses 15 cartridges of ink to print 10,000 pages. How many cartridges are needed for 30,000 pages?
  • A) 30
  • B) 35
  • C) 40
  • D) 45
  • E) 50
  1. If 20 bolts are used to assemble 4 chairs, how many bolts are needed for 20 chairs?
  • A) 80
  • B) 85
  • C) 90
  • D) 95
  • E) 100
  1. A construction company uses 60 tons of gravel to build 5 driveways. How much gravel is needed for 15 driveways?
  • A) 150
  • B) 170
  • C) 180
  • D) 190
  • E) 200
  1. A school requires 300 books for 15 classrooms. How many books are required for 45 classrooms?
  • A) 800
  • B) 850
  • C) 900
  • D) 950
  • E) 1000
  1. A tailor uses 25 yards of fabric to make 5 dresses. How many yards are needed for 15 dresses?
  • A) 60
  • B) 65
  • C) 70
  • D) 75
  • E) 80
  1. If a machine produces 200 widgets in 8 hours, how many widgets can it produce in 32 hours?
  • A) 600
  • B) 700
  • C) 800
  • D) 900
  • E) 1000
  1. A cook uses 2 kg of sugar to bake 5 cakes. How much sugar is needed to bake 25 cakes?
  • A) 8 kg
  • B) 10 kg
  • C) 12 kg
  • D) 14 kg
  • E) 16 kg
  1. A builder needs 45 planks of wood to make 3 tables. How many planks are required to make 9 tables?
  • A) 120
  • B) 125
  • C) 130
  • D) 135
  • E) 140
  1. If 10 gallons of paint cover 5 walls, how many gallons are needed to cover 20 walls?
  • A) 30
  • B) 35
  • C) 40
  • D) 45
  • E) 50
  1. A seamstress uses 3 meters of ribbon for 2 dresses. How many meters are needed for 10 dresses?
  • A) 10
  • B) 12
  • C) 13
  • D) 15
  • E) 16
  1. If 60 sheets of metal are used to make 10 doors, how many sheets are needed for 50 doors?
  • A) 200
  • B) 250
  • C) 300
  • D) 350
  • E) 400
  1. A workshop uses 100 nails for 25 pieces of furniture. How many nails are needed for 100 pieces of furniture?
  • A) 300
  • B) 350
  • C) 400
  • D) 450
  • E) 500
  1. If 8 bags of cement are used to make 4 foundations, how many bags are needed for 20 foundations?
  • A) 32
  • B) 36
  • C) 40
  • D) 44
  • E) 48
  1. A factory uses 200 liters of water to produce 500 units. How many liters are required to produce 2000 units?
  • A) 600
  • B) 700
  • C) 800
  • D) 900
  • E) 1000

Answers

  1. D) 240
  2. D) 48
  3. D) 30
  4. C) 450
  5. C) 2000
  6. C) 36
  7. E) 50
  8. A) 80
  9. C) 180
  10. C) 900
  11. D) 75
  12. C) 800
  13. B) 10 kg
  14. D) 135
  15. C) 40
  16. D) 15
  17. C) 300
  18. C) 400
  19. C) 40
  20. C) 800
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