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12 Nov 2024, 04:07
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There is only one way to select an ingredient or combination of ingredients that results in more than 20% fat.: False
The percentage of carbohydrate will always be more than 40% in a mix containing three or more ingredients.: False
A blend cannot include four ingredients.: False
The table below shows the composition of five ingredients as a percentage of four nutrients. These ingredients contain no other nutrients. When selecting ingredients to create a blend, they must either be used alone or combined in equal proportions. For example, if A, B, and C are chosen, they must be mixed in a 1:1:1 ratio. Regardless of the selection, the resulting blend must contain exactly 10% minerals.
For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False..
| Composition | ||||
| Ingredients | Carbohydrate | Protein | Fat | Mineral |
|---|---|---|---|---|
| A | 90 | 10 | 0 | 0 |
| B | 50 | 30 | 10 | 10 |
| C | 20 | 30 | 40 | 10 |
| D | 10 | 50 | 35 | 5 |
| E | 40 | 35 | 0 | 25 |
For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False..
| True | False | |
| There is only one way to select an ingredient or combination of ingredients that results in more than 20% fat. | ||
| The percentage of carbohydrate will always be more than 40% in a mix containing three or more ingredients. | ||
| A blend cannot include four ingredients. |
ShowHide Answer
Official Answer
There is only one way to select an ingredient or combination of ingredients that results in more than 20% fat.: False
The percentage of carbohydrate will always be more than 40% in a mix containing three or more ingredients.: False
A blend cannot include four ingredients.: False
12 Nov 2024, 04:07
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Official Solution:
Statement 1:
The requirement to be met is exactly 10% minerals.
Looking at the Minerals column (values: 0, 5, 10, 10, and 25), the possible ways to achieve this are:
1. Single ingredient: • B → Minerals = 10%, Fat = 10%. • C → Minerals = 10%, Fat = 40%.
2. Two ingredients: • B and C → Minerals = (10 + 10) / 2 = 10%, Fat = (10 + 40) / 2 = 25%.
3. Three ingredients: • A, D, and E → Minerals = (0 + 5 + 25) / 3 = 10%, Fat = (0 + 35 + 0) / 3 = 11.67%.
4. Four ingredients:
• A, B, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%, Fat = (0 + 10 + 35 + 0) / 4 = 11.25%.
• A, C, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%, Fat = (0 + 40 + 35 + 0) / 4 = 18.75%.
5. All five ingredients: • Minerals = (0 + 5 + 10 + 10 + 25) / 5 = 10%, Fat = (0 + 35 + 10 + 40 + 0) / 5 = 17%.
Since there are two ways to obtain more than 20% fat (C alone and B & C together), the first statement is False.
Statement 2:
The claim means that no valid combination of three or more ingredients should ever result in carbohydrates being 40% or less.
Checking carbohydrate content for valid selections:
Three ingredients:
• A, D, and E → Carbohydrates = (90 + 10 + 40) / 3 = 46.67%.
Since 46.67% is more than 40%, this combination satisfies the claim.
Four ingredients:
• A, B, D, and E → Carbohydrates = (90 + 50 + 10 + 40) / 4 = 47.5%.
Since 47.5% is more than 40%, this combination satisfies the claim.
• A, C, D, and E → Carbohydrates = (90 + 20 + 10 + 40) / 4 = 40%.
Since 40% is not more than 40%, this combination violates the claim.
Five ingredients:
• Carbohydrates = (90 + 10 + 40 + 20 + 50) / 5 = 42%.
Since 42% is more than 40%, this combination satisfies the claim.
Since we found one case (A, C, D, and E) where the carbohydrate percentage is exactly 40% and not more than 40%, the second statement is False.
Statement 3:
In the solution for the first statement, we found two cases where a combination of four ingredients resulted in exactly 10% minerals:
• A, B, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%.
• A, C, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%.
Since valid four-ingredient selections exist, the third statement is False.
Correct answer:
There is only one way to select an ingredient or combination of ingredients that results in more than 20% fat. "False"
The percentage of carbohydrate will always be more than 40% in a mix containing three or more ingredients. "False"
A blend cannot include four ingredients. "False"
Bunuel
Statement 1:
The requirement to be met is exactly 10% minerals.
Looking at the Minerals column (values: 0, 5, 10, 10, and 25), the possible ways to achieve this are:
1. Single ingredient: • B → Minerals = 10%, Fat = 10%. • C → Minerals = 10%, Fat = 40%.
2. Two ingredients: • B and C → Minerals = (10 + 10) / 2 = 10%, Fat = (10 + 40) / 2 = 25%.
3. Three ingredients: • A, D, and E → Minerals = (0 + 5 + 25) / 3 = 10%, Fat = (0 + 35 + 0) / 3 = 11.67%.
4. Four ingredients:
• A, B, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%, Fat = (0 + 10 + 35 + 0) / 4 = 11.25%.
• A, C, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%, Fat = (0 + 40 + 35 + 0) / 4 = 18.75%.
5. All five ingredients: • Minerals = (0 + 5 + 10 + 10 + 25) / 5 = 10%, Fat = (0 + 35 + 10 + 40 + 0) / 5 = 17%.
Since there are two ways to obtain more than 20% fat (C alone and B & C together), the first statement is False.
Statement 2:
The claim means that no valid combination of three or more ingredients should ever result in carbohydrates being 40% or less.
Checking carbohydrate content for valid selections:
Three ingredients:
• A, D, and E → Carbohydrates = (90 + 10 + 40) / 3 = 46.67%.
Since 46.67% is more than 40%, this combination satisfies the claim.
Four ingredients:
• A, B, D, and E → Carbohydrates = (90 + 50 + 10 + 40) / 4 = 47.5%.
Since 47.5% is more than 40%, this combination satisfies the claim.
• A, C, D, and E → Carbohydrates = (90 + 20 + 10 + 40) / 4 = 40%.
Since 40% is not more than 40%, this combination violates the claim.
Five ingredients:
• Carbohydrates = (90 + 10 + 40 + 20 + 50) / 5 = 42%.
Since 42% is more than 40%, this combination satisfies the claim.
Since we found one case (A, C, D, and E) where the carbohydrate percentage is exactly 40% and not more than 40%, the second statement is False.
Statement 3:
In the solution for the first statement, we found two cases where a combination of four ingredients resulted in exactly 10% minerals:
• A, B, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%.
• A, C, D, and E → Minerals = (0 + 10 + 5 + 25) / 4 = 10%.
Since valid four-ingredient selections exist, the third statement is False.
Correct answer:
There is only one way to select an ingredient or combination of ingredients that results in more than 20% fat. "False"
The percentage of carbohydrate will always be more than 40% in a mix containing three or more ingredients. "False"
A blend cannot include four ingredients. "False"
30 Jan 2025, 04:22
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
