Multiple choice

Passage

Directions: Refer to the data below and answer the question that follows. Jason organised the first 16 natural numbers into a 4 × 4 grid, placing one number in each cell of the grid. The rows of the grid were labelled A, B, C, and D (from top to bottom), while the columns were labelled P, Q, R, and S (from left to right). For instance, the number 9 was organised in cell AR. The total of the four numbers in rows B, C, and D was 29, 36, and 22, respectively. Similarly, the sum of the four numbers in columns P, Q, and R was 31, 23, and 44, respectively. The partially filled table is given below: P Q R S A 11 9 B 5 4 C 16 D 3 12

What is the average of the numbers in row A?

  1. 7.75

  2. 9.25

  3. 11.75

  4. 12.25

  5. a
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D Correct answer
Explanation

The sum of all numbers 1-16 is 136. Rows B+C+D sum to 29+36+22 = 87. Row A sum = 136 - 87 = 49. Average = 49/4 = 12.25.

AI explanation

The sum of the first 16 natural numbers is calculated using the formula n times (n plus 1) divided by 2, yielding 16 times 17 divided by 2, which equals 136. The total of rows B, C, and D is 29 plus 36 plus 22, giving a sum of 87. We subtract this from the overall total to find the sum of row A, so 136 minus 87 equals 49. To find the average of the four numbers in row A, we divide 49 by 4, which gives 12.25.

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