Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-47

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 \[=75+88=163\]