Two-digit number properties

CMAT 2024 · Quantitative Techniques & Data Interpretation · Easy · Number Systems

If the digit in the unit's place of a two-digit number is halved and the digit in ten's place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?

  1. A.

    Sum of the digits is a two-digit number.

  2. B.

    Digit in the unit's place is half of the digit in the ten's place.

  3. C.

    Digit in the unit's place and the ten's place are equal.

  4. D.

    Digit in the unit's place is twice the digit in ten's place.

Answer

D

Explanation

Let the two-digit number be 10x+y10x + y where xx is the tens digit and yy is the units digit. New number formed = 10(2x)+y2=20x+y210(2x) + \frac{y}{2} = 20x + \frac{y}{2}. Number obtained by interchanging digits = 10y+x10y + x. Given 20x+y2=10y+x  ⟹  19x=19y2  ⟹  y=2x20x + \frac{y}{2} = 10y + x \implies 19x = \frac{19y}{2} \implies y = 2x. Therefore, the digit in the units place (yy) is twice the digit in the tens place (xx).

Hence, Option D is correct.

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