A number exceeds 30% of itself by 49. The number is?

Appeared in: OSSSC Nursing Officer-2023

Explanation

The problem is solved by setting up an algebraic equation. Let the number be 'x'.
The statement 'A number exceeds 30% of itself by 49' translates to the equation: x - 0.30x = 49.
Simplifying the equation gives 0.70x = 49.
Solving for x by dividing 49 by 0.70 gives the answer, which is 70.

Option A: If the number is 56, then 30% of it is 16.8. The difference is 56 - 16.8 = 39.2, not 49.
Option B: If the number is 63, then 30% of it is 18.9. The difference is 63 - 18.9 = 44.1, not 49.
Option D: If the number is 210, then 30% of it is 63. The difference is 210 - 63 = 147, not 49. This value is significantly larger and likely results from a major calculation error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving algebraic word problems involving percentages as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, the underlying skill of translating words into calculations is critical in nursing.
Nurses frequently perform dosage calculations based on patient weight, drug concentrations, and prescribed amounts. An error in calculation can have severe patient safety consequences.
What if? If the problem stated the number was '49 more than 30% of itself', the approach would be the same (x = 0.30x + 49). However, if it said '30% of a number is 49', the equation would be 0.30x = 49, yielding a different answer.

How to Approach the Question

First, identify the unknown value and assign it a variable, such as 'x'.
Carefully read the problem to identify the relationship between the values. Keywords like 'exceeds', 'of', 'is', and 'by' are crucial.
Translate the words into a mathematical equation. '30% of itself' becomes '0.30x' and 'exceeds by 49' indicates a difference of 49.
Form the equation: x - 0.30x = 49.
Solve the algebraic equation for x.
Finally, check your answer by plugging it back into the original problem statement to ensure it holds true.

Concept Tested & Keywords

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Practise the full OSSSC Nursing Officer-2023

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