Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: What was Janet's score in the fourth physics test? (1) Her score in the fourth test was 12 points higher than her average (arithmetic mean) score in the first three tests. (2) Her score in the fourth test raised her average (arithmetic mean) test score from 87 to 90.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement (2) is sufficient: Let S3 be the sum of the first 3 tests. S3/3 = 87, so S3 = 261. Let x be the 4th test score. (261 + x)/4 = 90, so 261 + x = 360, x = 99. Statement (1) is not sufficient because it relates the score to the average, but the average is unknown.

AI explanation

Using the formula for a new average, statement (2) gives the equation (87 times 3 plus the fourth score) divided by 4 equals 90. Multiplying 90 by 4 yields a total of 360 points, and subtracting the initial total of 261 gives Janet a fourth test score of 99. Statement (1) only compares the fourth score to an unknown average, so it is insufficient. Thus, statement (2) alone is sufficient to answer the question.

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