Question

Find three consecutive odd integers such that the sum of first and third integers is same as the second integer when decreased by $9$.

• A. $-9,-7,-5$
• B. $-13,-11,-9$
• C. $-15,-13,-11$
• D. $-11,-9,-7$

Answer 1

Answer: (D)

$-11,-9,-7$

Let us say the first odd integer be $x$. The second consecutive odd integer would be $x+2$ (zit would not be $x+1$ because that would result in an even integer. The sum of two odd integers is even). The third consecutive odd integer would be $(x+2)+2$ or $x+4$.

Now, it is given that the sum of first and third integers is same as the second integer when decreased by $9$ which means:

$x+(x+4)=(x+2)-9\Rightarrow 2x+4=x-7\Rightarrow 2x-x=-7-4\Rightarrow x=-11$

Therefore, the first odd integer is $-11$ then the second integer is $x+2=-11+2=-9$ and the third integer is $x+4=-11+4=-7$

Hence, the three consecutive odd integers are $-11,-9,-7$.