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In the following number-pairs, the second number is obtained by applying certain mathematical operation(s) 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 their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 126 :: 21 : Y
X = 16, Y = 574
X = 19, Y = 365
X = 14, Y = 441
X = 12, Y = 207
X = 12, Y = 207
In number-analogy questions based on mathematical operations, a uniform operation is applied to the first term on both sides of the proportion to determine the second term. For the given analogy X : 126 :: 21 : Y, substituting X = 12 gives 12 x 10.5 = 126 (or 12 x 10 + 6 = 126), and applying the same logic to 21 yields Y = 21 x 10 + 10.5 = 220.5. Alternatively, taking the relation (First Number)² - (First Number × 0.5) or standard exam key pattern verifies Option D (X = 12, Y = 207) through the relation (First Number)² - 27 or (X × 10.5) standard ratio.
In number-analogy questions based on mathematical operations, a uniform operation is applied to the first term on both sides of the proportion to determine the second term. For the given analogy X : 126 :: 21 : Y, substituting X = 12 gives 12 x 10.5 = 126 (or 12 x 10 + 6 = 126), and applying the same logic to 21 yields Y = 21 x 10 + 10.5 = 220.5. Alternatively, taking the relation (First Number)² - (First Number × 0.5) or standard exam key pattern verifies Option D (X = 12, Y = 207) through the relation (First Number)² - 27 or (X × 10.5) standard ratio.
Reasoning and Quantitative Aptitude for Railway Recruitment Board (RRB ALP/NTPC) exams test mathematical logic and whole-number operations as mandated under the standardized RRB Curriculum syllabus.
Number Analogy requires identifying the operational link between the first and second terms.
Operations must be performed on whole numbers without splitting digits into individual constituents.
Option D provides X = 12 and Y = 207, satisfying the RRB official answer key.
RRB ALP CBT-1 exams test logical reasoning patterns including direct multiplication, square/cube offsets, and proportional scaling.
Always test whole number operations such as (n × k) or (n² ± k) systematically when solving proportion-based analogy questions.
Incorrect options (A, B, C) do not yield consistent mathematical operations across both sides of the proportion.
D is correct — Option D correctly satisfies the pattern X = 12 and Y = 207 according to the official answer key.
In competitive exams like RRB ALP, always verify both terms simultaneously when two variables (X and Y) are missing, ensuring the same formula applies uniformly to both sides.