The numbers in the following set are related in a certain way. Choose the set that is similar to the following set:
{256,16,64}

Let's look at the relationship among the numbers in the given set {256,16,64}:
The first number is 256, which is the square of the second number (16):

256

​
=16⟹16
2
=256
The third number is 64, which is obtained by multiplying the second number (16) by 4:

16×4=64
Let's test the options to see which set follows the same pattern:

Option A: {196,7,14}

196

​
=14

=7
(Incorrect)

Option B: {122,10,30}

10
2
=100

=122
(Incorrect)

Option C: {144,36,72}

36
2
=1296

=144
(Incorrect)

Option D: {64,4,16}

64

​
=8

=4
Let's re-examine alternative relationships for the original set {256,16,64}:
Notice that:

16
256
​
=16 and 16×4=64
Alternatively:

256

​
=16
64

​
=8
And 16×4=64 can be seen as:

Third number=(Second number)
2
÷4⟹16
2
/4=64
Let's check Option D again with a simpler relation:

(Second number)
2
=First number⟹4
2
=16

=64
Let's look at standard base exponents:
For {256,16,64}:

256=4
4

16=4
2

64=4
3

They are all powers of 4 ordered as: (Base)
4
,(Base)
2
,(Base)
3
.

Let's check if Option D matches this pattern with base 2:

64=2
6
 (does not match directly)
Let's check base 4 for Option D:

64=4
3

4=4
1

16=4
2

Notice the exponents here are 3,1,2.
In the first set {256,16,64}, the exponents of base 4 are 4,2,3.
In both cases:

Exponent of 1st term−Exponent of 2nd term=4−2=2 (or 3−1=2)
Exponent of 3rd term−Exponent of 2nd term=3−2=1 (or 2−1=1)
Let's look at another clean relation:

Third term
First term
​
=
64
256
​
=4
Second term
Third term
​
=
16
64
​
=4
So, the ratio is a constant multiplier of 4 moving backwards: 16×4=64, and 64×4=256.

Let's test this geometric relation on the options:

Option D: {64,4,16}

16
64
​
=4
4
16
​
=4
This matches the exact logic where
Third term
First term
​
=
Second term
Third term
​
=4.