In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 52, then the number is:  Choose one.
A) 11  B) 13  C) 24  D) 35  E) 46
Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2   Sum of digits = x + (x + 2) = 2x + 2   (11x + 2)(2x + 2) + (  + 2)= 
<gadget id="calculator">+ (  + 2)</gadget>
<output>2</output>
2x + 2   (11x + 2)(2x + 2)=52   22(x)(x) + 26x - 48 = 0   11(x)(x) +13x - 24 = 0   (x - 1)(11x +24) = 0   x = 1   Hence, required number = 11x + 2 = 13.   ANSWER:1311  + 2= 
<gadget id="calculator">11  + 2</gadget>
<output>13</output>
13.   ANSWER:13
<result>B</result>
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 52, then the number is: