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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 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 тАУ Operations on 13 such as adding/subtracting/multiplying 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: 32:: 18: Y
X=15, Y=37
X=13, Y=37
X=14, Y=35
X=13, Y=30
X=13, Y=37
Look for a consistent linear relationship of the form Y = 2X + n. In this case, the pattern is (Input * 2) + 6 = Output.
Look for a consistent linear relationship of the form Y = 2X + n. In this case, the pattern is (Input * 2) + 6 = Output.
Analyze the established pair
We are given the pair 18: Y. By observing the pattern 18 * 2 = 36, and adding 1, we get 37. Thus, the rule is (First Number * 2) + 1.
Apply the rule to the first pair
The first pair is X: 32. Using the rule (X * 2) + 6 = 32, we calculate 2X = 32 - 6, so 2X = 26, which means X = 13.
Re-evaluate the pattern consistency
Checking the option B (X=13, Y=37): If X=13, (13 * 2) + 6 = 32. If Y is the result of 18, applying a consistent operation logic (18 * 2) + 1 = 37. This pair satisfies the structure required by the question.
A: X=15 results in (152)+6=36 not 32; C: X=14 results in (142)+6=34 not 32; D: Y=30 does not follow the derived pattern (18*2)+1=37.
B is correct because the logic applied is (X * 2) + 6 = 32, which yields X = 13, and the consistent second pair operation yields 18 * 2 + 1 = 37.
When faced with number analogies where the operation is unknown, test both addition-subtraction patterns and multiplication-addition patterns simultaneously to save time.
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