There are some nectar-filled flowers on a tree and some bees are hovering on it. If one bee lands on each flower, one bee will be left out. If two bees land on each flower, one flower will be left out. The number of flowers and bees respectively are:

The correct option is 3 and 4, which means there are 3 flowers and 4 bees.

Let us break down the logical reasoning step-by-step to understand why this option is correct.

Let the number of flowers on the tree be represented by _f and the number of bees hovering around be represented by _b.

Case 1: One bee lands on each flower, leaving one bee out.
If each of the _f flowers has exactly 1 bee landing on it, the number of bees landed is _f.
Since 1 bee is left without a flower, the total number of bees _b must be 1 more than the number of flowers _f.
This gives us our first equation:
$b=f+1$

Case 2: Two bees land on each flower, leaving one flower out.
If the bees pair up and land on the flowers in groups of 2, they will occupy all but one flower.
The number of occupied flowers is:
$f-1$
Since each of these occupied flowers has 2 bees, the total number of bees _b is equal to 2 times the number of occupied flowers:
$b=2(f-1)$

Solving the Equations:
Now we can set the two expressions for _b equal to each other:
$f+1=2(f-1)$
Expand the right-hand side:
$f+1=2f-2$
Subtract _f from both sides:
$1=f-2$
Add 2 to both sides to find _f:
$f=3$

Now, substitute the value of _f back into the first equation to find _b:
$b=3+1=4$

Therefore, the number of flowers is 3 and the number of bees is 4.