Number System Ques 8
Question
There are three consecutive odd numbers and three consecutive even numbers. The smallest even number is 9 more than largest odd number. If the square of average of all the three given odd numbers is 507 less than the square of the average of all the three given even numbers, what is the smallest odd number?
(1) 11
(2) 13
(3) 17
(4) 19
(5) 9
(IBPS RRBs Officers CWE (Prelim Exam 09.09.2017) IInd Sitting)
Show Answer
Answer: (1)
Solution: (1)
Let the three consecutive odd numbers be $2 x+1,2 x+3$ and $2 x+5$.
$\therefore$ Three consecutive even numbers will be : $2 x+14,2 x+16$ and $2 x+18$.
According to the question,
$\left(\frac{2 x+14+2 x+16+2 x+18}{3}\right)^{2}$ $-\left(\frac{2 x+1+2 x+3+2 x+5}{3}\right)^{2}$ $=507$
$\Rightarrow(2 x+16)^{2}-(2 x+3)^{2}=507$
$\Rightarrow(2 x+16+2 x+3)(2 x+16-$ $2 x-3)=507$
$\Rightarrow(4 x+19) \times 13=507$
$\Rightarrow 4 x+19=\frac{507}{13}=39$
$\Rightarrow 4 x=39-19=20$
$\Rightarrow x=\frac{20}{4}=5$
$\therefore$ Smallest odd number $=2 x+1=2 \times 5+1=11$
BETA
