Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
What is the original number? (M.B.A., 2007) I. Sum of the two digits of a number is 10. The ratio between the two digits is 1 : 4. II. Product of two digits of a number is 16 and quotient of two digits is 4.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let the ten's and unit's digits be $x$ and $y$ respectively. Then, I. $x+y=10$ and $\frac{x}{y}=\frac{1}{4}$. II. $xy=16$ and $\frac{x}{y}=\frac{4}{1}$. ∴ II gives, $x^{2}=64 \Leftrightarrow x=8$. So, $4y=8 \Leftrightarrow y=2$. Thus, II alone gives the answer while I alone does not. ∴ The correct answer is (b).
Explanation as extracted from the printed page; notation may be imperfect.