Multiple choice

Directions: The following problem consists of a question and two statements, labelled (A) and (B), in which certain data is given. You have to consider the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in June or the meaning of counterclockwise) and then decide which out of these four options is correct for the given question. To earn a grade B in her English class, Esha must have an average score of 75 in her exams. She has taken four exams so far. What score must she get in the fifth exam to have an average of 75? (A) She averaged 70 in her first four exams. (B) If she gets an 80 in the fifth exam, her average will be 72.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient to answer the question asked.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient to answer the question asked.

  3. Both statements (A) and (B) together are sufficient to answer the question asked, but neither statement alone is sufficient.

  4. Each statement alone is sufficient to answer the question asked.

  5. Statements (A) and (B) together are not sufficient to answer the question asked, and additional data relevant to the problem is needed.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Target average = 75 for 5 exams, so total score = 375. (A) Average of 4 exams = 70, so sum = 280. 5th exam = 375 - 280 = 95. Sufficient. (B) If 5th = 80, average = 72. Total = 72 * 5 = 360. Sum of 4 exams = 360 - 80 = 280. 5th exam = 375 - 280 = 95. Sufficient.

AI explanation

Statement A provides the average of the first four exams as 70, meaning her total score for those four is 4 multiplied by 70, or 280. To achieve a final average of 75 across 5 exams, she needs a total score of 5 multiplied by 75, which is 375, so the required fifth exam score is 375 minus 280, equaling 95. Statement B states that an 80 on the fifth exam results in an average of 72, making the total score 5 multiplied by 72, or 360, which means the first four exams totaled 280. Since the required total is 375, the fifth exam score needed is 375 minus 280, or 95. Since either statement independently provides enough information to calculate the required score, each statement alone is sufficient to answer the question asked.

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