Question

A 2 digit number is less than 20. The sum of the digits is double than that of their product. what is the number?

Answer 1

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A $2$-digit number is less than $20.$ The sum of the digits is double than that of their product. what is the number?

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• A $2$-digit number is less than $20.$

• The sum of the digits is double than that of their product.

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The number.

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Let the ones digit be $x.$

Since the $2$-digit number is less than $20,$ it's unit digit must be one.

According to condition,

$2×1×x = x+1$

$⇒2x = x+1$

$⇒2x-x = 1$

$⇒x = 1$

So, $x = 1.$

The number

$= (10×1)+x$

$= 10+x$

Substitute $x$ with $1.$

$10+x$

$= 10+1$

$= 11$

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The number $= 11$

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The number is $11.$

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