The sum of five consecutive numbers is 250. What is the difference between the sum of the smallest and the largest number and the square of the middle number? |
A) 2500
B) 2200
C) 2000
D) 2600
E) None of these
Correct Answer: E
Solution :
Let the five consecutive numbers be x, \[x+1,\]\[x+2,\]\[x+3,\] and \[x+4,\] respectively, |
Then, \[x+x+1+x+2+x+3+x+4=250\] |
\[\Rightarrow \] \[5x+10=250\] |
\[\Rightarrow \] \[5x=250-10\] |
\[\Rightarrow \] \[5x=240\]\[\Rightarrow \]\[x=\frac{240}{5}=48\] |
Middle number \[=48+2=50\] |
\[\therefore \] Required difference \[={{50}^{2}}-48-52=2400\] |
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