If 12$3 = 51, 14$2 = 43, 16$4 = 79, then what is the value of 17$3?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The problem presents a pattern where the symbol '$' represents a specific set of mathematical operations.
The pattern is identified by analyzing the given examples: the product of the two numbers is added to a constant value of 15.
The rule is: a$b = (a × b) + 15.
Applying this rule to 17$3: (17 × 3) + 15 = 51 + 15 = 66.

Option B: This value might be the result of a calculation error, such as adding 10 instead of 15 to the product (51 + 10 = 61).
Option C: This is the result of only the first part of the operation (17 × 3) without adding the constant 15.
Option D: This value could be a result of a simple miscalculation or adding an incorrect constant, like 3 (51 + 3 = 54).

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.
While not a clinical question, pattern recognition is a crucial cognitive skill for nurses.
Nurses use pattern recognition to identify subtle changes in a patient's condition, interpret vital sign trends, and recognize early signs of complications.
For example, recognizing a pattern of gradually decreasing blood pressure, increasing heart rate, and low urine output can help a nurse identify early signs of shock.

How to Approach the Question

First, analyze the given equations to find a consistent mathematical relationship between the numbers on both sides of the '$' symbol.
Start by testing basic operations. Notice that the product of the numbers (e.g., 12 × 3 = 36) is related to the final result (51).
Formulate a hypothesis. In this case, the difference between the product and the result is a constant: 51 - 36 = 15.
Test this hypothesis, (a × b) + 15, on all the other given examples to ensure it is the correct rule.
Once the rule is confirmed, apply it to the question 17$3.
Calculate (17 × 3) + 15 to arrive at the final answer and select the corresponding option.

Concept Tested & Keywords

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Practise the full DSSSB -28 August 2019 (Shift-2)

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