Insert the missing number: [Matrix Grid] 2 5 2 3 4 3 1 2 4 36 197 ?

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The puzzle follows a column-wise pattern where the number in the last row is derived from the numbers above it.
The specific operation is the sum of the cubes of the first three numbers in the column.
For the third column, the numbers are 2, 3, and 4.
The calculation is 2³ + 3³ + 4³ = 8 + 27 + 64.
The sum is 99, which is the missing number.

Option A: This is an incorrect calculation. It does not follow the established pattern of summing the cubes of the numbers in the column.
Option C: This is an incorrect calculation. It might be the result of an arithmetic error, such as adding the numbers and multiplying by a constant, but it does not fit the sum of cubes pattern.
Option D: This is an incorrect calculation. It is close to the correct answer but does not result from the correct application of the sum of cubes rule (8 + 27 + 64 = 99).

Visual 1: Infographic: A visual breakdown of the matrix, showing each column with arrows pointing downwards. Each arrow is labeled with the 'sum of cubes' operation (e.g., 2³+3³+1³) leading to the result at the bottom.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning - Matrix Puzzles as background academic context rather than a clinical decision trigger.
This type of question does not test clinical knowledge but assesses logical reasoning and problem-solving skills, which are essential for nurses.
Strong analytical skills help nurses in interpreting patient data, identifying patterns in symptoms, and making sound clinical judgments under pressure.
What if the pattern was row-wise? If the pattern was row-wise, you would test operations (addition, subtraction, multiplication, etc.) on the numbers 2, 5, and 2 to see if a logical sequence exists, and then apply it to the other rows. In this case, the pattern is clearly vertical.

How to Approach the Question

First, carefully observe the grid of numbers. Look for a potential pattern or relationship between the numbers.
Test for patterns column-wise (vertically). Check if an arithmetic operation (addition, subtraction, multiplication, division, squares, cubes) on the first few numbers in a column produces the last number.
In this case, for Column 1: Test 2+3+1=6 (Incorrect). Test 231=6 (Incorrect). Test 2²+3²+1²=4+9+1=14 (Incorrect). Test 2³+3³+1³=8+27+1=36 (Correct).
Verify this pattern with the second column: 5³+4³+2³ = 125+64+8 = 197. The pattern holds true.
Apply the confirmed pattern to the third column to find the missing number: 2³+3³+4³ = 8+27+64 = 99.
Select the option that matches your calculated result.

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer 2016 (Shift -2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.