A number has two digits. The digit in the tens place is 2 more than the digit in the ones place. The sum of the digits is 1/6 of the number. So the number is:

1. A

   54

2. B

   46

3. C

   108

4. D

   64

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

• The problem is solved by translating the two given conditions into a system of two linear equations with two variables.
• Let 't' be the tens digit and 'u' be the ones digit. The equations are: 1) t = u + 2 and 2) t + u = (1/6)(10t + u).
• Solving this system yields u = 8 and t = 10.
• The number is constructed as 10t + u, which calculates to 10(10) + 8 = 108.
• Although the problem mentions a 'two-digit' number, the algebraic solution results in 108, which is an option and satisfies both mathematical conditions.

Why Other Options Were Wrong

• Option A: For the number 54, the tens digit (5) is not 2 more than the ones digit (4). It fails the first condition.
• Option B: For the number 46, the tens digit (4) is not 2 more than the ones digit (6). It fails the first condition. It also fails the second condition, as 4+6=10, but 46/6 is not 10.
• Option D: For the number 64, the first condition is met (6 = 4 + 2). However, the second condition fails. The sum of digits is 6 + 4 = 10, but 1/6 of the number is 64/6, which is approximately 10.67, not 10.

Related Visual

• Visual 1: Flowchart: A flowchart can illustrate the logical steps to solve the problem: 1. Read the problem and define variables (t, u). 2. Translate conditions into equations (t = u+2; t+u = (10t+u)/6). 3. Solve the system of equations. 4. Calculate the final number. 5. Verify the solution.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations derived from a word problem as background academic context rather than a clinical decision trigger.
• This question assesses mathematical and logical reasoning skills, which are foundational for nurses.
• Nurses frequently use algebra for critical calculations, such as determining drug dosages, calculating IV drip rates, and interpreting patient data, where precision is vital for patient safety.
• What if the fraction was 1/7 instead of 1/6? The equations would be t=u+2 and 7(t+u)=10t+u. Solving this gives u=2 and t=4, making the number 42. This shows how a small change in a parameter can significantly alter the outcome, emphasizing the need for careful attention to detail in nursing calculations.

How to Approach the Question

• First, carefully read the problem to identify the unknowns and the conditions. Here, the unknown is a number with two digits.
• Assign variables to represent the unknown digits. For example, let 't' be the tens digit and 'u' be the ones digit. The number itself is then represented as 10t + u.
• Translate each condition given in the word problem into a separate mathematical equation involving your variables.
• You should now have a system of two equations with two variables. Use an algebraic method, such as substitution or elimination, to solve for the variables.
• Once you find the values of the digits, construct the number.
• Finally, check your answer against the original conditions and the given options. Note any inconsistencies, such as the 'two-digit' constraint versus a three-digit result, and choose the answer that follows from the mathematical derivation.

Concept Tested & Keywords

• Concept Tested: Solving a system of linear equations derived from a word problem.
• Stem keywords: two digits, tens place, ones place, sum of the digits, 1/6 of the number
• Lead-in keywords: the number is

Question ID

QE8IfT74J9ULgRU_Km6lkC

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