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

7×2+12+43=14

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

Explanation

The core task is to identify the correct underlying mathematical structure from a garbled input and then test the given options.
The interpreted equation is 7 × 2 + 12 ÷ 4 - 3 = 14, which is correct.
Interchanging the numbers 4 and 3 gives the new equation 7 × 2 + 12 ÷ 3 - 4 = 14.
Following the BODMAS rule, this new equation evaluates to 14 + 4 - 4 = 14, which simplifies to 14 = 14.
This is the only interchange that results in a correct equation.

Option B: Interchanging 12 and 3 creates the equation 7 × 2 + 3 ÷ 4 - 12 = 14. This evaluates to 14 + 0.75 - 12 = 2.75, which is not equal to 14.
Option C: Interchanging 7 and 3 creates the equation 3 × 2 + 12 ÷ 4 - 7 = 14. This evaluates to 6 + 3 - 7 = 2, which is not equal to 14.
Option D: Interchanging 7 and 4 creates the equation 4 × 2 + 12 ÷ 7 - 3 = 14. This evaluates to approximately 8 + 1.71 - 3 = 6.71, which is not equal to 14.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests logical and mathematical reasoning, specifically the ability to correct a flawed equation by interchanging numbers as background academic context rather than a clinical decision trigger.
While this is a general reasoning question, the underlying skills are crucial in nursing.
Nurses must be meticulous and apply rules-based thinking for tasks like medication dosage calculations, where a misplaced number or a misread operator can have serious consequences.
This exercise strengthens attention to detail and logical problem-solving, which are essential for safe and effective patient care.

How to Approach the Question

First, analyze the given equation 7×2+12+43=14. Recognize that it's likely presented in a confusing or incorrect format.
Attempt to reconstruct a logical mathematical equation from the given numbers and symbols. The most plausible interpretation is 7 × 2 + 12 ÷ 4 - 3 = 14.
Verify your reconstructed equation using the order of operations (BODMAS/PEMDAS).
Systematically test each option. For each choice, perform the indicated number interchange in your corrected equation.
Recalculate the value of the new equation for each option.
The correct answer is the option that results in a true mathematical statement (e.g., 14 = 14).

Concept Tested & Keywords

Concept Tested: This question tests logical and mathematical reasoning, specifically the ability to correct a flawed equation by interchanging numbers.
Stem keywords: numbers, interchanged, equation, mathematically correct
Lead-in keywords: Which two

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