If the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?  Answers.
A) 50
B) 53
C) 49
D) 48
E) 44
Sum of 5 Integer (a, b, c, d, e) = 5*45= 
<gadget id="calculator">5*45</gadget>
<output>225</output>
225   e - a= 10   i.e. e = a+10   For e to be maximum remaining 4 MUST be as small as possible   Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers   i.e. a+a+a+a+(a+10) = 225   i.e. 5a = 215   i.e. a = 43   i.e. Largest e = 43+10= 
<gadget id="calculator">43+10</gadget>
<output>53</output>
53   Answer: option 53
<result>B</result>
If the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?