Which two numbers should be interchanged to make the below equation mathematically correct?
28 ÷ 7 × 6 - 3 + 10 = 16

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

Explanation

The core concept is the order of operations, commonly remembered by the acronym BODMAS/PEMDAS.
Interchanging 6 and 3 transforms the equation to: 28 ÷ 7 × 3 - 6 + 10.
Following BODMAS, we first perform division: 28 ÷ 7 = 4.
Next, multiplication: 4 × 3 = 12.
Finally, addition and subtraction from left to right: 12 - 6 = 6, and 6 + 10 = 16.
This result matches the right-hand side of the equation, making this the correct interchange.

Option A: Interchanging 6 and 10 results in the expression 28 ÷ 7 × 10 - 3 + 6. Following BODMAS, this evaluates to (4 × 10) - 3 + 6 = 40 - 3 + 6 = 43, which is not 16.
Option B: Interchanging 3 and 10 results in the expression 28 ÷ 7 × 6 - 10 + 3. Following BODMAS, this evaluates to (4 × 6) - 10 + 3 = 24 - 10 + 3 = 17. This is very close to 16 but incorrect.
Option D: Interchanging 7 and 3 results in the expression 28 ÷ 3 × 6 - 7 + 10. Following BODMAS, this evaluates to (28/3) × 6 - 7 + 10 = 56 - 7 + 10 = 59, which is not 16.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Evaluating mathematical expressions using the BODMAS/PEMDAS rule as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, the underlying principle of procedural accuracy is paramount in nursing.
Nurses must perform calculations for drug dosages, IV drip rates, and fluid balances. A mistake in the order of operations (e.g., confusing multiplication with division) can lead to significant medication errors, potentially harming the patient.
For example, calculating a weight-based medication dose requires multiplying the dose (mg/kg) by the patient's weight (kg) and then dividing by the drug concentration (mg/mL). Performing these steps out of order would result in an incorrect and dangerous dose.

How to Approach the Question

First, understand the goal: You need to find which pair of numbers, when swapped, will make the final equation equal to 16.
Recall the correct order of mathematical operations using the BODMAS/PEMDAS rule: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Remember that Division/Multiplication and Addition/Subtraction are performed from left to right.
Calculate the result of the original, unchanged equation to confirm it's incorrect. This helps you understand the starting point.
Methodically test each option provided. For each option, rewrite the equation with the two numbers interchanged.
Carefully apply the BODMAS rule to the new equation and calculate the final result.
Compare the result with the target value (16). The option that yields 16 is the correct answer.

Concept Tested & Keywords

Concept Tested: Evaluating mathematical expressions using the BODMAS/PEMDAS rule.
Stem keywords: numbers, interchanged, equation, mathematically correct
Lead-in keywords: Which two numbers

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

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