1. The problem involves matching the given weights of rectangular tiles with the amounts used for testing and determining the sample sizes. 2. We have eight tile weights: 0.512 kg, 0.272 kg, 0.68 kg, 0.6 kg, 1.28 kg, 1.6 kg, 0.064 kg, and 0.024 kg. 3. The four amounts used for testing are 0.136 kg, 0.256 kg, 0.32 kg, and 0.12 kg. 4. To find the sample size for each test amount, divide the test amount by the weight of each tile to see which division yields an integer (indicating exact count of tiles). 5. For 0.136 kg: checking division by weights: - 0.136 ÷ 0.024 = 5.666... (Not integer) - 0.136 ÷ 0.032 (not given, ignore) - 0.136 ÷ 0.064 = 2.125 (Not integer) - 0.136 ÷ 0.068 (not given, ignore) No exact integer fits with the given weights for 0.136 kg; may involve partial tiles or approximation. 6. For 0.256 kg: - 0.256 ÷ 0.064 = 4 (integer, so 4 tiles of 0.064 kg) 7. For 0.32 kg: - 0.32 ÷ 0.16 (not given) - 0.32 ÷ 0.272 = 1.176 (No) - 0.32 ÷ 0.32 (not in given weights) - 0.32 ÷ 0.16 (not given) - 0.32 ÷ 0.08 (not given) No exact integer. 8. For 0.12 kg: - 0.12 ÷ 0.024 = 5 (integer, so 5 tiles of 0.024 kg) 9. Given the data, matching test amounts with tiles weights for integral multiples can only be done confidently for 0.256 kg and 0.12 kg test amounts. 10. Final answer: For 0.256 kg, sample size is 4 tiles of 0.064 kg each. For 0.12 kg, sample size is 5 tiles of 0.024 kg each. For 0.136 kg and 0.32 kg, sample sizes cannot be determined exactly from the given weights.