The average of three consecutive odd numbers is 12 more than one-third of the first of these numbers. What is last of the three numbers? [SSC (CQL) 2011] |
A) 15
B) 17
C) 19
D) 21
Correct Answer: C
Solution :
Let the smallest number be \[(2x-1).\]Then, consecutive number are \[(2x+1),\]\[(2x+3).\] |
According to the question, |
\[\frac{(2x-1)+(2x+1)+(2x+3)}{3}=\left( \frac{2x-1}{3} \right)+12\] |
\[\Rightarrow \] \[2x+1=\frac{2x-1+36}{3}\] |
\[\Rightarrow \] \[6x+3=2x+36-1\] |
\[\Rightarrow \] \[4x=32\]\[\Rightarrow \]\[x=\frac{32}{4}=8\] |
\[\therefore \]Third number \[=(2x+3)=(2\times 8+3)=19\] |
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