Select the missing term from the given options.

90 : 360 :: 40 : 160 :: ? : 120

The correct answer is 30.

Step-by-step Explanation:

This question is based on a number analogy where each pair of numbers maintains the exact same ratio relationship.

Step 1: Analyze the first pair (90 : 360)

Determine the relationship between 90 and 360 by dividing the second number by the first number:

$\frac{360}{90}=4$

This shows that the second number is 4 times the first number:

$90\times 4=360$

Step 2: Verify with the second pair (40 : 160)

Test the same rule on the second pair:

$\frac{160}{40}=4$

Again, multiplying the first number by 4 yields the second number:

$40\times 4=160$

Step 3: Apply the pattern to find the missing term (? : 120)

Let the missing term be represented by $x$.

Using the established pattern:

$x\times 4=120$

Now, solve for $x$:

$x=\frac{120}{4}=30$

Therefore, the missing term is 30.