A two-digit number has 3 as its units digit, and the sum of its digits equals one-seventh of the number itself. What is the number?
Aptitude
Linear Equation
Difficulty: Easy
Choose an option
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A43
-
B53
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C63
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D73
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E83
Answer
Correct Answer: 63
Explanation
Introduction: Represent the number using its tens digit and the fixed units digit 3. The given condition links the sum of digits to one-seventh of the number, producing a simple linear equation in the tens digit.
Given Data / Assumptions:
- Number = 10t + 3.
- Sum of digits = t + 3 = (1/7)(10t + 3).
- Digits are 0–9 and t ≠ 0.
Concept / Approach: Multiply both sides to clear the fraction; solve for t. Substitute back to obtain the number and verify.
Step-by-Step Solution:
t + 3 = (10t + 3)/7 → 7t + 21 = 10t + 3.18 = 3t → t = 6.Number = 10*6 + 3 = 63.Verification / Alternative check: Sum of digits 6 + 3 = 9; one-seventh of 63 = 9, condition satisfied.
Why Other Options Are Wrong: 43, 53, 73, 83 do not satisfy the one-seventh condition.
Common Pitfalls: Forgetting to multiply both sides by 7 or miscomputing the sum of digits.
Final Answer: 63