Question: 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?
Options:
A) 15
B) 17
C) 19
D) 21
Show Answer
Answer:
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}=( \frac{2x-1}{3} )+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 $