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Two-Part Analysis questions test your ability to evaluate two related components of a problem, requiring logical reasoning and mathematical skills to solve interdependent conditions. |
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Read the question stem carefully, identify the relationship between the two parts, and focus on simplifying the problem to avoid unnecessary calculations. |
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X = 6, y = 4. Adding the equations gives 2x = 12, so x = 6. Subtracting gives 2y = 8, so y = 4. |
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These questions often provide a problem with two blanks and a set of paired answer choices, each representing a combination of possible solutions. |
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Speed = Distance / Time. Example: If a car travels 100 miles in 2 hours, its speed is 100/2 = 50 mph. |
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A company has to assign 10 workers to two projects. The first project requires 6 workers, and the second project requires 4 workers. How many ways can this be done? |
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What is the most efficient way to analyze numerical Two-Part Analysis questions? |
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Break the question into smaller parts and solve one blank at a time while keeping the relationship between the two parts in mind. |
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A person invests $10,000 in two accounts, one earning 5% interest and the other earning 8% interest. If the total interest earned is $700, how much was invested in each account? |
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What is the best way to eliminate answer choices in Two-Part Analysis questions? |
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Use logical reasoning to quickly rule out inconsistent or impossible pairs that violate the conditions of the question. |
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A = 10, b = 10. Substituting b = 20 - a into the second equation gives a = 10 and b = 10. |
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What is the importance of interpreting language in Two-Part Analysis questions? |
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Precise interpretation ensures that you understand the conditions correctly and avoid misreading the relationships between the parts. |
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If the product of two numbers is 72 and their sum is 18, what are the two numbers? |
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Why is checking consistency between the two parts crucial in solving these questions? |
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Consistency ensures that the chosen answers satisfy all given constraints and logical dependencies. |
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A train travels 60 miles at a speed of 30 mph and another 120 miles at a speed of 40 mph. What is the average speed for the entire journey? |
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The average speed is 36 mph. Total distance is 180 miles, total time is 5 hours, so 180/5 = 36. |
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If two people can complete a task together in 6 hours and one of them takes 9 hours alone, how long will the other take to complete the task alone? |
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The other person will take 18 hours. Their combined rate is 1/6, one person's rate is 1/9, so the other's rate is 1/6 - 1/9 = 1/18. |