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15 Mar 2026, 16:03
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
21% (02:04) correct
79%
(01:57)
wrong
based on 34
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When the point totals for 20 participants were recorded, three mistakes were made: one was off by 10 points, another by 7 points, and a third by 2 points. Was the percent error in the reported total number of points greater than 5 percent?
(1) The average of the reported scores was 15.
(2) The difference between the reported total and the actual total was 15 points.
(1) The average of the reported scores was 15.
(2) The difference between the reported total and the actual total was 15 points.
16 Mar 2026, 01:27
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This is a classic Data Sufficiency setup. Let me work through whether each statement gets us to a yes/no answer about percent error > 5%.
What we know: 20 participants, three errors of +10, +7, and -2 (or -10, -7, +2). Total error could be 10+7+2 = 19 or 10+7-2 = 15 or other combos depending on direction.
Statement 1: Average of reported scores = 15
If average = 15, then reported total = 20 × 15 = 300.
But we don't know the actual total, so we can't calculate percent error. Not sufficient alone.
Statement 2: Difference between reported and actual total = 15 points
So the error is 15 points. Percent error = (15 / actual total) × 100%.
But without knowing the actual total, we can't determine if this is > 5%.
Actually wait, the errors must sum to 15. So actual total could be 300/0.95 ≈ 316 (if 5% error). Since the error is fixed at 15, and we need to know if 15/actual > 5%, we're stuck without more info. Not sufficient alone.
Together: From (1), reported total = 300. From (2), actual differs by 15. So actual = 285 or 315.
If actual = 315: error % = 15/315 ≈ 4.8% (not > 5%)
If actual = 285: error % = 15/285 ≈ 5.3% (YES > 5%)
Wait, that's two different answers. This means we can't determine a single yes/no. The answer should be E - Statements 1 and 2 together are not sufficient, because the direction of the error matters (whether the reported total is 15 over or 15 under).
Answer: E
What we know: 20 participants, three errors of +10, +7, and -2 (or -10, -7, +2). Total error could be 10+7+2 = 19 or 10+7-2 = 15 or other combos depending on direction.
Statement 1: Average of reported scores = 15
If average = 15, then reported total = 20 × 15 = 300.
But we don't know the actual total, so we can't calculate percent error. Not sufficient alone.
Statement 2: Difference between reported and actual total = 15 points
So the error is 15 points. Percent error = (15 / actual total) × 100%.
But without knowing the actual total, we can't determine if this is > 5%.
Actually wait, the errors must sum to 15. So actual total could be 300/0.95 ≈ 316 (if 5% error). Since the error is fixed at 15, and we need to know if 15/actual > 5%, we're stuck without more info. Not sufficient alone.
Together: From (1), reported total = 300. From (2), actual differs by 15. So actual = 285 or 315.
If actual = 315: error % = 15/315 ≈ 4.8% (not > 5%)
If actual = 285: error % = 15/285 ≈ 5.3% (YES > 5%)
Wait, that's two different answers. This means we can't determine a single yes/no. The answer should be E - Statements 1 and 2 together are not sufficient, because the direction of the error matters (whether the reported total is 15 over or 15 under).
Answer: E
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