Number Logic Puzzle Explained

This problem involves identifying a pattern or logical relationship between pairs of numbers and then applying that same logic to find a missing number.

Analyzing Given Number Pairs

We are given two examples of this relationship:

• 100 is related to 18.
• 90 is related to 16.

Our task is to find which number among the options (60, 80, 65, 70) follows the same logic when related to 12.

Deriving the Mathematical Relationship

Let's denote the first number in the pair as 'N' and the second number as 'R' (Result). We need to find a function f such that R = f(N).

Pair 1: N = 100, R = 18

Let's try to find a mathematical operation linking 100 and 18.

Consider dividing N by 5:

Calculation: $ \frac{100}{5} = 20 $

This value, 20, is close to 18. The difference is $ 20 - 18 = 2 $. So, maybe the formula is $ R = \frac{N}{5} - 2 $. Let's check.

Check: $ \frac{100}{5} - 2 = 20 - 2 = 18 $. This matches the first pair.

Pair 2: N = 90, R = 16

Let's test the same formula $ R = \frac{N}{5} - 2 $ with the second pair.

Calculation: $ \frac{90}{5} - 2 = 18 - 2 = 16 $

This also matches the second pair. So, the logic is confirmed.

Applying Logic to Find the Missing Number

The question asks: "Which of the following is related to 12 using the same logic?" This means the Result (R) is 12, and we need to find the corresponding Number (N) from the options.

We use the formula $ R = \frac{N}{5} - 2 $ with R = 12.

Set up the equation:

$$ \frac{N}{5} - 2 = 12 $$

Now, solve for N:

1. Add 2 to both sides: $$ \frac{N}{5} = 12 + 2 $$ $$ \frac{N}{5} = 14 $$
2. Multiply both sides by 5: $$ N = 14 \times 5 $$ $$ N = 70 $$

So, the number 70 is related to 12 using the established logic.

Verifying the Options

Let's check if applying the logic $ R = \frac{N}{5} - 2 $ to the given options yields a result of 12.

Conclusion

Based on the derived logic $ R = \frac{N}{5} - 2 $, the number 70 when related to 12 satisfies the pattern.