Difficulty: Medium
Correct Answer: 48
Explanation:
Introduction / Context:
Number analogy questions test your skill in spotting arithmetic patterns between numbers. In this problem you are given the pair 12 and 39 and asked to extend the same rule to the number 15. Such questions often involve simple operations like multiplication, addition, or subtraction, but you must test them systematically rather than guessing based on superficial similarity.
Given Data / Assumptions:
- The first pair is 12 and 39, where 39 is derived from 12 by some consistent arithmetic rule.
- The second starting number is 15, and you must find which option gives the corresponding output under the same rule.
- The options are 48, 52, 39, and 51, all of which are reasonably close in value to what might come from simple operations on 15.
- We assume ordinary integer arithmetic without hidden tricks such as digit reversal or number bases unless clearly suggested.
Concept / Approach:
The main strategy is to identify a pattern that transforms 12 into 39. Once you discover a simple and reasonable rule, you apply the same transformation to 15 and see which option matches. It is important to check that the rule you choose is natural and not overly complicated, because exam questions are designed around straightforward ideas such as multiplying by a fixed number and then adding or subtracting another fixed value.
Step-by-Step Solution:
Step 1: Test simple multiplication: 12 * 2 = 24, 12 * 3 = 36, 12 * 4 = 48, none of which is exactly 39.Step 2: Try combining multiplication and addition. If 12 * 3 = 36, adding 3 more gives 39, so one possible rule is result = (number * 3) + 3.Step 3: Confirm this rule fits the first pair: for 12, (12 * 3) + 3 = 36 + 3 = 39, which matches the given second number exactly.Step 4: Apply the same rule to 15: (15 * 3) + 3 = 45 + 3 = 48.Step 5: Among the options, 48 appears and therefore is the only value consistent with the discovered pattern.
Verification / Alternative check:
Check quickly whether any other simple rule could connect 12 to 39 and 15 to some other option. For example, if you tried 12 * 4 - 9, you would get 39, but then 15 * 4 - 9 gives 51, which is also one of the options. However, this rule is less natural than multiplying by 3 and adding 3, because 12 * 3 already gives a value close to 39. Most test setters prefer patterns where the multiplier is small and the additional constant is also small and intuitive. The (number * 3) + 3 rule is clean and symmetric and is therefore the more reasonable choice.
Why Other Options Are Wrong:
- 52: There is no simple consistent combination of multiplication and a small constant that maps 12 to 39 and then 15 to 52 without becoming arbitrary.- 39: This would incorrectly suggest that 15 also maps to 39, ignoring the difference between the starting numbers, so it does not extend the pattern logically.- 51: Although an artificial rule could be constructed to reach 51, it is less straightforward than the rule that produces 48 from 15 using multiplication by 3 and addition of 3.
Common Pitfalls:
One common mistake is to jump at the first arithmetic pattern that fits the first pair without checking whether it gives a sensible result for the second number. Another pitfall is overcomplicating the rule with multiple operations when a simpler one exists. To avoid these issues, always look for the smallest and cleanest formula that works for the given pair, then apply it consistently to the new number and cross check with all options.
Final Answer:
Using the pattern result = (number * 3) + 3, 12 maps to 39 and 15 maps to 48. Hence the correct answer is 48.
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