Find the value of q. (q-2)² = [(19-8) ÷ 11 + (1/2 × 48)]

Appeared in: DSSSB 14 August 2024

Explanation

The problem requires solving for the variable 'q' in the equation (q-2)² = [(19-8) ÷ 11 + (1/2 × 48)].
Following the BODMAS/PEMDAS rule, the right-hand side simplifies: [(11) ÷ 11 + 24] → [1 + 24] → 25.
The equation becomes (q-2)² = 25.
Taking the square root of both sides gives q - 2 = ±5.
This results in two possible values for q: q = 7 (from q - 2 = 5) and q = -3 (from q - 2 = -5).
Comparing these results with the given options, the value 7 is the correct answer.

Option A: The value 5 is incorrect. This might be obtained if one incorrectly solves q - 2 = 5 as q = 5, forgetting to add 2 to both sides.
Option B: The value 2 is incorrect. This might be obtained by mistakenly setting the expression (q-2) to zero.
Option D: The value 9 is incorrect. This could result from a calculation error, such as adding 2 to 7 again (7+2=9) or incorrectly solving the square root.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a quadratic equation using the BODMAS/PEMDAS rule for simplification as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, strong numeracy skills are fundamental for nurses.
Nurses constantly perform calculations for drug dosages, IV drip rates, and fluid balance monitoring, where accuracy is critical for patient safety.
What if the equation was (q-2)² = -25? In this case, there would be no real number solution for q, as the square of a real number cannot be negative. This concept is important in understanding data that falls outside expected ranges.

How to Approach the Question

First, carefully read the equation and identify the unknown variable you need to solve for, which is 'q'.
Recall the order of operations: BODMAS/PEMDAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). This dictates the sequence for simplifying expressions.
Focus on the right-hand side of the equation first. Systematically solve the operations within the brackets, starting with the innermost parentheses.
Once the right-hand side is simplified to a single number, you will have a simpler equation of the form (q-2)² = value.
To isolate 'q', take the square root of both sides. Remember that the square root of a positive number has both a positive and a negative solution (e.g., √25 = ±5).
Solve for 'q' for both the positive and negative roots to find all possible values.

Concept Tested & Keywords

Concept Tested: Solving a quadratic equation using the BODMAS/PEMDAS rule for simplification.
Stem keywords: Find the value of q, (q-2)², BODMAS, PEMDAS
Lead-in keywords: Find the value

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Practise the full DSSSB 14 August 2024

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