Find the fit for unsolved equation from the following options? 5 x 6 x 3 = 356, 1 x 0 x 5 = 510, 5 x 6 x 7= ______?

Appeared in: NCL (MP) Nursing Officer - 2019

Explanation

The puzzle follows a logical rearrangement pattern, not mathematical multiplication.
For an equation 'a x b x c', the result is formed by concatenating the digits in the order 'c', 'a', 'b'.
In the equation '5 x 6 x 7', 'a' is 5, 'b' is 6, and 'c' is 7.
Applying the 'cab' pattern gives '756'.

Option A: This option (567) represents the original order of the numbers ('abc'), which does not match the established pattern.
Option B: This option (657) follows the pattern 'bac' (second, first, third number), which is inconsistent with the logic derived from the examples.
Option C: This option (210) is the result of standard mathematical multiplication (5 × 6 × 7 = 210). The puzzle is based on logic, not arithmetic.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning and Pattern Recognition as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and pattern recognition, which are fundamental cognitive skills.
In nursing, these skills are crucial for interpreting patient data, recognizing trends in vital signs, and making sound clinical judgments under pressure.
What if the pattern was 'bca'? If the pattern were 'bca', the answer for 5 x 6 x 7 would be 675, as 'b' is 6, 'c' is 7, and 'a' is 5.

How to Approach the Question

First, analyze the given examples: '5 x 6 x 3 = 356' and '1 x 0 x 5 = 510'.
Recognize that standard multiplication is not being used (e.g., 5 × 6 × 3 = 90, not 356). This signals a logic or pattern-based puzzle.
Examine the relationship between the numbers on the left side (the inputs) and the number on the right side (the output).
Identify the pattern: the output number is formed by rearranging the input numbers. Specifically, the third number comes first, followed by the first, and then the second (c, a, b).
Verify this pattern with the second example ('1 x 0 x 5 = 510'). The pattern holds true.
Apply the confirmed pattern to the unsolved equation '5 x 6 x 7' to find the missing number (756).

Concept Tested & Keywords

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Practise the full NCL (MP) Nursing Officer - 2019

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