Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
What is the value of the two-digit number? (Bank P.O., 2009) I. The product of the digits is 72 and the difference between the digits is 1. II. The digit at the unit place is greater than the other.
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 digit be $x$ and the unit's digit be $y$. II. $y>x$. I. $xy=72$ and $y-x=1$ or $y=x+1 \Leftrightarrow x(x+1)=72 \Leftrightarrow x^{2}+x-72=0 \Leftrightarrow x^{2}+9x-8x-72=0 \Leftrightarrow x(x+9)-8(x+9)=0 \Leftrightarrow (x+9)(x-8)=0 \Leftrightarrow x=8$. So, $y=x+1=9$. ∴ Required number $=89$. Thus, both I and II together give the answer. ∴ The correct answer is (e).
Explanation as extracted from the printed page; notation may be imperfect.