Difficulty: Easy
Correct Answer: 19/4
Explanation:
Introduction / Context:
This question is a numerical analogy problem from quantitative aptitude. You are given one pair of related numbers, 2.25 and 13/4, and then asked to find the missing term that will complete the proportion 2.25 : 13/4 :: 3.75 : ?. Such questions test whether you can recognise a simple arithmetic or fractional relationship and then apply the same pattern consistently to a new pair of numbers, rather than guessing randomly from the options.
Given Data / Assumptions:
We are given the pair 2.25 and 13/4.
We are given the starting number 3.75 in the second pair, and must find its related term.
The relationship between the first pair is assumed to be the same as the relationship between the second pair.
The answer choices are 17/4, 19/4, 15/4, 11/4, and 21/4, of which exactly one must satisfy the same pattern.
Concept / Approach:
For number analogies with decimals and fractions, a good strategy is to convert all decimals into fractions with the same denominator so that the pattern becomes visible. Once we see how 2.25 is connected to 13/4, we can apply the same rule to 3.75. In many exam questions the pattern is a simple addition, subtraction, multiplication, or division rather than something overly complicated.
Step-by-Step Solution:
Step 1: Convert 2.25 into a fraction. We know that 2.25 = 225/100 = 9/4.Step 2: Compare 9/4 with 13/4. The denominators are the same, so look at the numerators: 13 - 9 = 4.Step 3: Therefore, 13/4 = 9/4 + 4/4, meaning we have added 1 to 2.25 in its fractional form, because 4/4 = 1.Step 4: Now convert 3.75 into a fraction. We have 3.75 = 375/100 = 15/4.Step 5: Apply the same operation, adding 1. So 15/4 + 1 = 15/4 + 4/4 = 19/4.Step 6: Check the options. The fraction 19/4 is listed, so it is the only value that follows the same pattern as in the first pair.
Verification / Alternative check:
Another way to think about it is in terms of decimals. We already saw that 2.25 corresponds to 3.25, which is 13/4. This is simply 2.25 + 1. Similarly, 3.75 plus 1 equals 4.75. If we convert 4.75 into a fraction, we get 4.75 = 475/100 = 19/4, which perfectly matches the value we identified earlier. Both fractional and decimal approaches confirm the same answer.
Why Other Options Are Wrong:
Option 17/4 would correspond to 4.25 in decimal form, which is 0.5 more than 3.75, not 1 more, so it does not match the original pattern of adding 1.
Option 15/4 is just 3.75 itself, meaning no change at all, whereas the first pair clearly involved an increase of 1.
Option 11/4 corresponds to 2.75 and would require subtracting 1 from 3.75 rather than adding 1, which reverses the relationship.
Option 21/4 equals 5.25, which would mean adding 1.5, again inconsistent with the original pair where we added exactly 1.
Common Pitfalls:
Candidates sometimes compare raw decimals without converting them to fractions, which can hide simple relationships like equal denominators or equal increments. Another frequent mistake is to look for multiplication or division patterns first and overlook straightforward addition or subtraction. Finally, it is important not to guess based merely on approximate decimal sizes but instead to verify the exact arithmetic relationship between the two pairs.
Final Answer:
Therefore, the number that correctly completes the analogy 2.25 : 13/4 :: 3.75 : ? is 19/4.
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