Four pairs of numbers have been given out of which three are alike in some manner, while one is different. Choose the odd one.
36 : 13
Pair Analysis Method
The task requires us to identify the pair of numbers that does not fit a pattern shared by the other pairs. We need to carefully examine each pair to find a common mathematical link.
Analyzing Each Number Pair
Let's denote each pair as A : B and investigate the relationship between A and B.
- Pair 1: 54 : 17
We check if there's a relationship involving multiplication and addition. Let's try multiplying the second number (B=17) by 3 and adding 3.
Calculation: $3 \times 17 + 3 = 51 + 3 = 54$.
The result, 54, matches the first number (A) in the pair. So, this pair fits the pattern $A = 3B + 3$.
- Pair 2: 36 : 13
We apply the same potential pattern, $A = 3B + 3$, to this pair.
Calculation: $3 \times 13 + 3 = 39 + 3 = 42$.
The first number in the pair is 36. Since $36 \neq 42$, this pair does not follow the pattern $A = 3B + 3$.
- Pair 3: 90 : 29
Let's test the pattern $A = 3B + 3$ again.
Calculation: $3 \times 29 + 3 = 87 + 3 = 90$.
The result, 90, matches the first number (A). This pair fits the pattern $A = 3B + 3$.
- Pair 4: 72 : 23
We test the pattern $A = 3B + 3$ one more time.
Calculation: $3 \times 23 + 3 = 69 + 3 = 72$.
The result, 72, matches the first number (A). This pair also fits the pattern $A = 3B + 3$.
Identifying the Pattern Across Pairs
After analyzing all the pairs, we can see a consistent pattern ($A = 3B + 3$) in three of them: 54 : 17, 90 : 29, and 72 : 23. The pair 36 : 13 is the only one that deviates from this rule.
Here's a summary of our findings:
| Pair (A : B) | Relationship Check ($3B + 3$) | Does it match A? |
|---|---|---|
| 54 : 17 | $3 \times 17 + 3 = 54$ | Yes |
| 36 : 13 | $3 \times 13 + 3 = 42$ | No (A is 36) |
| 90 : 29 | $3 \times 29 + 3 = 90$ | Yes |
| 72 : 23 | $3 \times 23 + 3 = 72$ | Yes |
Determining the Odd Pair
The pair 36 : 13 is identified as the "odd one out" because it does not satisfy the mathematical relationship $A = 3B + 3$ that holds true for the other pairs.
Conclusion on the Odd Pair
Based on the consistent pattern found in the majority of the pairs, the unique pair is 36 : 13.
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