Directions:

Determine the missing number pair to complete the given sequence:

(4, 16), (7, 28), (10, 40), ?, (16, 64)

The correct option is (13, 52).

To find the missing number pair, let us analyze the pattern in the given sequence of pairs:

$(4,16),(7,28),(10,40),?,(16,64)$

Let each pair be represented as $(x,y)$.

Pattern for the first number ($x$):
The first number in each pair increases by $3$ at each step:

$4+3=7$

$7+3=10$

$10+3=13$

$13+3=16$

So, the first number of the missing pair is $13$.

Pattern for the second number ($y$):
The second number in each pair is $4$ times the first number ($y=4\times x$):

$4\times 4=16$

$7\times 4=28$

$10\times 4=40$

$13\times 4=52$

$16\times 4=64$

Alternatively, the second number increases by $12$ at each step ($16+12=28$, $28+12=40$, $40+12=52$, $52+12=64$).

Therefore, the missing number pair is (13, 52).