Using the flowchart below, what value when entered for Y will generate a mathematical error and prevent our flowchart from being completely executed?

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BlackTom AI · Accepted Answer

Restating the problem to ensure understanding: Using the flowchart, identify which input value for Y will cause a mathematical error and stop the flowchart from completing.
Option set to consider: [0, 3, None of these values will produce a mathematical error, 1].
First, I will walk through the flow of the program steps in a general sense before plugging in any candidate Y values.
- Step 1: Y = Y x 5 multiplies the current Y by 5.
- Step 2: Y = Y - 15 subtracts 15 from the updated Y.
- Step 3: The decision node checks whether Y/15 ≥ 2. This involves a division operation, dividing the current Y by 15.
- Step 4: If the condition is true (yes path), the flow outputs Y + 2; if false (no path), it outputs Y - 4.

Key point: A mathematical error in this flow would occur if any operation within the path cannot be performed, such as a division by zero. In this flow, the division operation is Y/15. Since 15 is a constant, division by zero would only occur if the denominator were zero. But the denominator here is 15, which never becomes zero through the prior steps (multiplying by 5 and then subtracting 15 will not change the fact that the divisor is 15).
Now, let’s test the candidate values one by one:
- Testing Y = 0:
  - Step 1: Y = 0 x 5 = 0
  - Step 2: Y = 0 - 15 = -15
  - Step 3: Evaluate (-15) / 15 = -1, and -1 ≥ 2 is false, so we take the no branch.
  - Step 4: Output would be Y - 4, i.e., -15 - 4 = -19.
  There is no mathematical error here; the division is well-defined.
- Testing Y = 3:
  - Step 1: Y = 3 x 5 = 15
  - Step 2: Y = 15 - 15 = 0
  - Step 3: Evaluate 0 / 15 = 0, and 0 ≥ 2 is false, so we take the no branch.
  - Step 4: Output would be Y - 4, i.e., 0 - 4 = -4.
  Again, no mathematical error occurs; division is defined.
- Testing Y = 1:
  - Step 1: Y = 1 x 5 = 5
  - Step 2: Y = 5 - 15 = -10
  - Step 3: Evaluate (-10) / 15 ≈ -0.666..., and -0.666... ≥ 2 is false, so we take the no branch.
  - Step 4: Output would be Y - 4, i.e., -10 - 4 = -14.
  No mathematical error occurs; division is defined for -10 divided by 15.

Observations about the structure: In all three test cases, the division by 15 is performed with a nonzero divisor (15) and yields a real number; there is no step that would create a division by zero, since the divisor is constant and cannot become zero due to the prior operations. Since none of the tested inputs cause an undefined operation, these particular values do not produce a mathematical error.
Considerational note: The option 'None of these values will produce a mathematical error' would be true if no input from the provided options causes a division by zero or other undefined operation in the flow. The other options (0, 3, 1) each lead to well-defined computations throughout the flow for the division and the subsequent outputs.
In summary, evaluating each candidate input shows that the flow can proceed without encountering a mathematical error, indicating that the problematic case is not among the listed values. Therefore, among the given choices, the ones that would cause a math error do not appear to be present, and the option asserting that none of these values will produce a mathematical error appropriately captures that outcome.
If you want to verify further, you could test additional Y values to confirm that division by 15 remains defined at every step, but with a constant nonzero divisor, division by zero cannot occur merely from the transformation Y = Y x 5 and Y = Y - 15.

(72ab92) AP CS Principles 2.1 AP-Style MC Practice

Using the flowchart below, what value when entered for Y will generate a mathematical error and prevent our flowchart from being completely executed?

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