The ages of three friends are prime numbers. The sum of the ages is less than 51. If the ages are in Arithmetic Progression (AP) and if at least one of the ages is greater than 10, what is the difference between the maximum possible median and minimum possible median of the ages of the three friends?  Choose the correct answer.
A) 0	B) 1	C) 13	D) 6	E) 8
Let the numbers are a-d, a , a+d   sum &lt;51 =&gt; a-d+a+a+d &lt; 51 =&gt; middle number a &lt;17   prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47   a can be 3,5,7,11,13   if a is 3 -&gt; a-d can be 2 only; a+d not possible thus reject this.   if a is 5, a-d can be 2 and 3; only a-d = 3 satisfies   =&gt; three numbers can be 3,5,7 -&gt;reject this , as it is given at least one is &gt;10   if a = 7 ; a-d can be 3 and a+d can be 11   This satisfies all the conditions hence the median is 7=&gt; min median.   if a = 11, the three element pair is 3,11,19 or 5,11,17   median = 11; we are not sure if its the max median possible   if a = 13, 7,13,19 pair is possible   median = 13; reject 11 as the max.   thus difference = 13-7= 
<gadget id="calculator">13-7</gadget>
<output>6</output>
6   ANSWER:6
<result>D</result>
The ages of three friends are prime numbers. The sum of the ages is less than 51. If the ages are in Arithmetic Progression (AP) and if at least one of the ages is greater than 10, what is the difference between the maximum possible median and minimum possible median of the ages of the three friends?