Special Two Digit Number

Algebra Level 2

A 2-digit number's ten's place is twice its unit digit. It must be divisible by:

7 only 3 and 7 neither 3 nor 7 3 only

Rajen Kapur by Rajen Kapur , 72, India

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1 solution

Gabe Smith
Nov 6, 2015

Let the units digit be A A so the tens digit is 2 A . 2A. That means that the number can be expressed as 10 × ( 2 A ) + 1 × ( A ) = 20 × A + A = 21 × A . 10 \times (2A) + 1\times (A) = 20\times A+A = 21\times A.

Since 21 = 3 × 7 , 21=3\times 7, 21 × A 21\times A must be divisible by both 3 and 7.

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