Which two signs should be interchanged to make the below equation mathematically correct?

$$15 + 3 - 4 \times 5 \div 3 = 18$$

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

This question requires applying the order of operations (BODMAS/PEMDAS) to test different sign interchanges.
The original equation is 15 + 3 - 4 × 5 ÷ 3 = 18.
Interchanging + with ÷ and - with × gives the new equation: 15 ÷ 3 × 4 - 5 + 3.
Solving this new equation: (15 ÷ 3) × 4 - 5 + 3 becomes 5 × 4 - 5 + 3, which simplifies to 20 - 5 + 3, then 15 + 3, resulting in 18.
This matches the right-hand side of the equation, confirming it as the correct solution.

Option B: Interchanging only the + and - signs results in the equation 15 - 3 + 4 × 5 ÷ 3. Following BODMAS, this calculates to 12 + (20 ÷ 3) which is approximately 12 + 6.67 = 18.67, not 18.
Option C: This is identical to the previous option. Interchanging - and + is the same operation as interchanging + and -. The result is 18.67, not 18.
Option D: Interchanging × and + signs gives 15 × 3 - 4 + 5 ÷ 3. Following BODMAS, this calculates to 45 - 4 + (5 ÷ 3), which is approximately 41 + 1.67 = 42.67, not 18.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mathematical Reasoning and Order of Operations (BODMAS/PEMDAS) as background academic context rather than a clinical decision trigger.
While not a direct clinical question, mathematical proficiency is a fundamental nursing skill required for safe medication administration.
Nurses frequently calculate drug dosages, IV drip rates, and solution concentrations. An error in the order of operations can lead to significant medication errors.
What if? If a nurse miscalculated a dosage for a potent drug like heparin or insulin due to an order-of-operations error, it could lead to a severe adverse event, such as hemorrhage or hypoglycemia. This highlights the critical importance of mathematical accuracy in practice.

How to Approach the Question

First, identify the goal: find which pair of sign interchanges makes the equation true.
Systematically test each option provided. For each option, rewrite the equation with the interchanged signs.
Apply the BODMAS/PEMDAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) to evaluate the new equation.
Work from left to right for operations with the same priority (i.e., Division and Multiplication, or Addition and Subtraction).
Continue testing options until you find the one that results in a true statement (LHS = RHS).
In this case, the first option tested (+ with ÷, - with ×) yields 18 = 18, so it is the correct answer.

Concept Tested & Keywords

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E6 Nursing Fundamentals Taylor p. 916-918

Practise the full DSSSB - 29 August 2019 (Shift-2)

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