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Five numbers $10,7,5,4$ and $2$ are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.
2. The second number from the left is exactly half of the left-most number.
3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

1. $2$
2. $4$
3. $7$
4. $10$

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1. No two odd or even numbers are next to each other.
2. The second number from the left is exactly half of the left-most number.
So, the left most number must be even and its half must be odd which comes next. Only options are $10,5$
3. The middle number is exactly twice the right-most number.
Middle number must be even and only options left are $2$ and $4$. Since $1$ is not there, $4$ must be the middle and $2$ the right most.

Thus we get $$10\quad 5 \quad 4 \quad 7 \quad 1$$

Required answer is $7.$

Option C.

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