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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of:: is the same as that on the right side of::? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) X:38::9:Y
X = 14, Y = 28
X = 14, Y = 30
X = 15, Y = 48
X = 15, Y = 28
X = 14, Y = 28
Look for the mathematical relationship between the numbers. Here, the rule is (x┬▓ + 2) = y. For 9, 9┬▓ + 2 = 83 (not in options). Alternatively, check the relationship between the two pairs: X: 38 and 9: Y. Notice the inverse square relationship: 6┬▓ + 2 = 38, so X = 6. 3┬▓ = 9. Wait, the pattern is: (X┬▓ + 2) = 38 => X = 6. Let's re-evaluate: Maybe it's (X * X) + 2. If X=6, 36+2=38. If Y follows a pattern from 9... check other options.
Look for the mathematical relationship between the numbers. Here, the rule is (x┬▓ + 2) = y. For 9, 9┬▓ + 2 = 83 (not in options). Alternatively, check the relationship between the two pairs: X: 38 and 9: Y. Notice the inverse square relationship: 6┬▓ + 2 = 38, so X = 6. 3┬▓ = 9. Wait, the pattern is: (X┬▓ + 2) = 38 => X = 6. Let's re-evaluate: Maybe it's (X * X) + 2. If X=6, 36+2=38. If Y follows a pattern from 9... check other options.
Analyze the Structure
The problem provides a proportionality: X : 38 :: 9 : Y. We need to find X and Y such that the internal relation is consistent.
Verify Option A (X=14, Y=28)
If X=14 and Y=28, the pairs are 14: 38 and 9: 28. In the first pair, 14 * 2 + 10 = 38. In the second, 9 * 2 + 10 = 28. Both follow the rule (n * 2 + 10 = result).
B: (14, 30) gives 142+10=38 but 92+10=28!= 30. C: (15, 48) gives 152+10=40!= 38. D: (15, 28) gives 152+10=40!= 38.
A is correct because both pairs satisfy the consistent mathematical operation of multiplying the first number by 2 and adding 10 to obtain the second number (142+10=38 and 92+10=28).
In number analogy questions, if a direct square or cube rule doesn't fit, test basic linear transformations like (n * a) + b.
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