Question

What can be placed at ‘?’ if both sides of ‘::’ have the same relationship between numbers:
85 : 42 :: 139 : ?

• A. 68
• B. 69
• C. 70
• D. 67

Hint:

In analogies where the second number is roughly half of the first, always test patterns like $(n \pm 1) / 2$ or $n / 2 \pm c$ first.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Number analogy questions are a staple of General Aptitude Tests (GAT). They require the candidate to identify a hidden mathematical logic, rule, or pattern that connects the first pair of numbers and then apply that identical logic to find the missing term in the second pair. The relationships can range from basic arithmetic (addition, subtraction, multiplication, division) to more complex operations involving squares, cubes, prime numbers, or digit-based manipulation.
Step 2: Key Formula or Approach:
In this specific case, we observe the magnitude of the change. The number decreases from 85 to 42. Usually, such a significant drop suggests a division or a combination of subtraction and division. Let the relationship be defined as:
\[ \text{Second Number} = \frac{\text{First Number} - \text{constant}}{2} \]
Step 3: Detailed Explanation:
1. Analyzing the First Ratio (85 : 42):
We start with the number 85. If we try to divide 85 by 2 directly, we get 42.5. Since the target is 42, it implies a small subtraction before the division.
Calculation:
\[ 85 - 1 = 84 \]
Now, dividing the result by 2:
\[ 84 \div 2 = 42 \]
This confirms the logic: \( (\text{Number} - 1) / 2 \).
2. Applying the Pattern to the Second Ratio (139 : ?):
Now, we take the third number, which is 139, and apply the exact same mathematical sequence.
First, subtract 1 from 139:
\[ 139 - 1 = 138 \]
Next, divide this resulting value by 2:
\[ 138 \div 2 = 69 \]
3. Alternative Logic Verification:
We can also look at this from the reverse direction. If we multiply the second number by 2 and add 1, we should get the first number.
Checking the first pair: \( (42 \times 2) + 1 = 84 + 1 = 85 \). (Matches)
Checking the second pair with the proposed answer: \( (69 \times 2) + 1 = 138 + 1 = 139 \). (Matches)
Since 69 is present in the options as (B), the logic is robust and verified.
Step 4: Final Answer:
By applying the identified pattern \( (x - 1) / 2 \), we determine that 139 relates to 69.