Multiple choice

A total of 30 students are arranged in a grid for morning assembly, with 6 rows and 5 columns. Each of the 30 positions in the grid represents the height of a student. The average height (in cm) of the students in row i is Ri (1 ≤ i ≤ 6). The average height of the students in column j is Cj (1 ≤ j ≤ 5). What is the value of R6? (1) C1 + C2 + C3 + C4 + C5 = 850 (2) R1 + R2 + R3 + R4 + R5 = 850

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

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

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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C Correct answer
AI explanation

Statement 1 provides the sum of the column averages (850), but because R6 is a row average, statement 1 alone cannot determine its value. Statement 2 provides the sum of the row averages for the first five rows (850), but without the total sum of all row averages, R6 remains undetermined. By combining both statements, you find the overall average is 850 / 5 = 170, making the total sum of all heights 170 * 30 = 5100; since the sum of the first five rows is 5 * 850 = 4250, the sum for R6 is 850, yielding an R6 value of 850 / 5 = 170. Both statements together are sufficient, but neither statement alone is sufficient.

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