Question

a two digit number is less than 20. The sum of the digits is double that of their product. What is the number?
A)12
B)15
C)13
D)11
please elaborate on the answer
(A question from International Maths Olympiad)

Answer 1

Let the numbers be x and y.

x+y = 2xy
y=2xy-x
x(2y-1) = y
x = y/(2y-1). Here if y=1, x=1.
Thus the number = 11.



I hope this will help you

Answer 2

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

A) 12

B) 15

C) 13

D) 11

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Solution⫸}}}}}}$

Let the ones digit be x.

Since the number is of 2 -digits and is less than 20, it's tens digit must be 1.

According to condition,

x+1 = 2×1×x

⇒ x+1 = 2x

⇒ 1 = 2x-x

⇒ 1 = x

So, x = 1.

The number

= (10×1)+x

= 10+x

Substitute x with 1.

10+x

= 10+1

= 11

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Therefore⫸}}}}}}$

The required number is 11.

Correct option is D) 11.

${\huge\mathfrak \pink{Done࿐}}\\{\huge\mathfrak \green{Hope\:this\: helps\:you.}}\\{\huge\mathfrak \orange{Have\:a\: nice\:day.}}$