The sum of 8 consecutive odd numbers is 656. Also, average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? [Bank of Baroda (P0) 2011] |
A) 165
B) 175
C) 163
D) 180
E) None of the above
Correct Answer: C
Solution :
Here, let the first odd number be x. |
Then, 8 consecutive odd numbers are as |
\[x-8,\]\[x-6,\]\[x-4,\]\[x-2,\]\[x,\] |
\[x+2,\]\[x+4,\]\[x+6\] |
Now, \[x-8+x-6+x-4+x-2+x+x\] |
\[+\,\,2+x+4+x+6=656\] |
\[\Rightarrow \]\[8x-8=656\]\[\Rightarrow \]\[8x=656+8\] |
\[\Rightarrow \]\[8x=664\]\[\Rightarrow \]\[x=83\] |
Smallest odd number \[=86-8=78\] |
Now, let four consecutive even numbers be |
\[y-2,\]\[y,\]\[y+2\] and \[y+4.\] |
Now, \[4y+4=87\times 4\]\[\Rightarrow \]\[4y+4=348\] |
\[\Rightarrow \]\[4y=344\]\[\Rightarrow \]\[y=86\] |
Now, smallest even number \[=86-8=78\] |
Second largest even number \[=88\] |
\[\therefore \]Sum of both the number \[=75+88=163\] |
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