The sum of 8 consecutive odd numbers is 656. Also, average of four consecutive even number is 87. What is the sum of the smallest odd number and second largest even number? |
A) 165
B) 175
C) 163
D) Cannot be determined
E) None of the above
Correct Answer: C
Solution :
Let the 8 consecutive odd numbers be |
\[x,\]\[x+2,\]\[x+4,\]\[x+6,\]\[x+8,\]\[x+10,\]\[x+12\] and \[x+14,\]respectively. |
Then, \[x+(x+2)+(x+4)+(x+6)+(x+8)\] |
\[+\,(x+10)+(x+12)+(x+14)=656\] |
\[\Rightarrow \] \[8x+56=656\] |
\[\Rightarrow \] \[x=\frac{600}{8}=75\] |
Let the four consecutive even numbers be |
\[x,\]\[x+2,\]\[x+4,\]\[x+6,\] respectively. |
Then, \[x+(x+2)+(x+4)+(x+6)=4\times 87\] |
\[\Rightarrow \] \[4x+12=4\times 87\] |
\[\Rightarrow \] \[4x=348-12\] |
\[\Rightarrow \] \[x=\frac{336}{4}=84\] |
\[\therefore \]Second largest even number |
\[=x+4=84+4=88\] |
Hence, the required sum \[=75+88=163\] |
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