10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range U of the 10 numbers? Answers.
A) 25  B) 27  C) 30  D) 52  E) 55
Positions: 1 2 3 4 5 6 7 8 9 10   Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b   y - x = 25   Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.   b - a = 30 --&gt; b = 30 + a   In order to increase the range, we have to maximize the value of 'b'.   'b' can be maximized by taking the max value of 'a'.   From the assumed values, maximum value of 'a' can be 22.   Therefore, b = 30 + 22= 
<gadget id="calculator">30 + 22</gadget>
<output>52</output>
52   Range U= 52 - 0= 
<gadget id="calculator">52 - 0</gadget>
<output>52</output>
52   Answer: 52
<result>D</result>
10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range U of the 10 numbers?