“A number is greater than 30% of itself by 49. What is the number?”

NORCET 9 Prelims-2025

Reasoning

Medium

Appeared in: NORCET 9 Prelims-2025

Explanation

The first step is to translate the word problem into an algebraic equation. Let the unknown number be 'x'.
The statement 'a number is greater than 30% of itself by 49' translates to the equation: x = (0.30 * x) + 49.
To solve for x, rearrange the equation by subtracting 0.30x from both sides, which simplifies to 0.70x = 49.
Dividing 49 by 0.70 gives the value of x, which is 70.
To verify, calculate 30% of 70 (which is 21) and check the difference: 70 - 21 = 49. This confirms the answer is correct.

Option A: This value (56) is 80% of the correct answer (70). It does not satisfy the condition that the number minus 30% of itself equals 49 (56 - 0.3*56 = 39.2).
Option B: This value (63) is 90% of the correct answer (70). This might result from an arithmetic error where 1 - 0.30 is incorrectly calculated as 0.90. The condition is not met (63 - 0.3*63 = 44.1).
Option D: This value (210) is obtained by multiplying the correct answer by 3 (70 * 3). This likely stems from misinterpreting '30%' or the relationship in the problem.

Visual 1: No visual is required for this type of mathematical calculation question.

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 aptitude question, strong numeracy skills are essential for nurses for accurate medication dosage calculations, interpreting lab results, and managing fluid balances.
For example, calculating a drug dose based on body weight (mg/kg) or titrating an IV drip rate (mL/hr) requires similar mathematical precision and understanding of percentages.
What if? If the number was greater than 20% of itself by 40, the equation would be x - 0.20x = 40. This simplifies to 0.80x = 40, and solving for x gives 50. This demonstrates how the same logical steps apply to different values.

How to Approach the Question

Step 1: Read the problem carefully to understand the relationship between the quantities. Identify the unknown value and assign it a variable, such as 'x'.
Step 2: Translate the words into a mathematical equation. 'Percent of' means multiplication (e.g., 30% of x is 0.30x). 'Greater than... by' indicates a difference.
Step 3: Set up the equation. 'A is greater than B by C' can be written as A - B = C. In this case, A is the number (x), B is 30% of the number (0.30x), and C is 49. The equation is x - 0.30x = 49.
Step 4: Solve the algebraic equation for the variable 'x'. Combine the 'x' terms first (1x - 0.30x = 0.70x) and then isolate x.
Step 5: After finding x, plug the value back into the original problem statement to verify that it holds true. This helps catch any calculation errors.

Concept Tested & Keywords

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