In this set, each subsequent fraction is half the size of the preceding fraction; (the denominator is doubled for each successive fraction, but the numerator stays the same). Given that the last fraction in the set is \(\displaystyle \frac{1}{16}\), it follows that the subsequent fraction will be \(\displaystyle \frac{1}{32}\). 

A prime number only has two factors, one and itself.  \(\displaystyle 13\) and \(\displaystyle 23\) are the only values given that have that property.  But the range of the set is between \(\displaystyle 1\) and \(\displaystyle 20\) which means that the answer cannot be \(\displaystyle 23\) since it is greater than \(\displaystyle 20\).  That means the final answer is \(\displaystyle 13\).

The equation for the average would be 

\(\displaystyle \frac{8+9+x+11+13}{5}=10.2\).

To work backwards you must first multiple both sides by \(\displaystyle 5\).  

This gives us \(\displaystyle 8+9+x+11+13=51\).  

To solve for \(\displaystyle x\), you must subtract all the other values from \(\displaystyle 51\).  

This gives us an answer of \(\displaystyle x=10\).

The numbered cards in a deck range from \(\displaystyle 2\) to \(\displaystyle 10\).  

Since \(\displaystyle 10\) is not in the above set, it is the missing NUMBER card from the deck.

King and Ace are incorrect choices as they are called face cards in a deck of cards.

Add 5 to the first element to get the second element. The increment increases by two with each successive entry. The pattern can be seen below:

\(\displaystyle 6\bold{ + 5} = 11\)

\(\displaystyle 11\textbf{+7} = 18\)

\(\displaystyle 18 \bold{+9} = 27\)

\(\displaystyle 27\textbf{+11} = 38\)

\(\displaystyle 38 \textbf{+13} = 51\) - this is the correct response

This is confirmed by noting:

\(\displaystyle 51 \textbf{+15} = 66\)

There are three things going on with these patterns.

First, the number of dots in the pattern is increasing by one, so there must be four dots in the correct choice. However, this does not eliminate any of the choices.

Second, the sector that included the dots alternates between lower right and upper left, so the correct choice must have its dots in the upper left sector. This eliminates figures (c) and (d) and leaves (a) and (b) as possible choices.

Third, the shaded sector is rotating clockwise. The shaded sector in the correct choice must be the one at the lower left, thereby eliminating (b) and leaving (a) as the correct choice.

Taking only shapes into account, the sequence is:

Triangle, circle, square,

Triangle, circle, square,

Triangle, ?

To continue the cycle, the next shape must be a circle.

Now, taking only coloration into account, the sequence is:

Left half shaded, unshaded,

Top half shaded, unshaded,

Left half shaded, unshaded,

Top half shaded, ?

To continue the cycle, the next shape must be unshaded.

Therefore, the correct choice is the unshaded circle, Figure (c).

Taking only shapes into account, the sequence is:

Triangle(s), square(s). circle(s),

Triangle(s), square(s). circle(s),

Triangle(s)...

To continue the pattern, the next figure must comprise one or two squares.

Taking only number and color of shapes into account, the sequence is

One white, one black over one white, one black, one white over one black,

One white, One black over one white, one black,...

To continue the pattern, the next figure must comprise one white shape over one black. 

Therefore, the correct choice is one white square over one black square, which is Figure (b).

The way to get from one entry of the sequence to the next alternates between multiplying by two and adding one, as follows:

\(\displaystyle 18 \bold { \times 2} = 36\)

\(\displaystyle 36 \bold{ +1} = 37\)

\(\displaystyle 37\bold { \times 2 } = 74\)

\(\displaystyle 74 \textbf{+1} = 75\)

\(\displaystyle 75 \bold { \times 2} = 150\)

Continuing the pattern:

\(\displaystyle 150 \bold{ +1} = 151\)

\(\displaystyle 151 \bold { \times 2} = 302\), the correct choice.