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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:114::26:Y
X=31,Y=72
X=39,Y=86
X=38,Y=78
X=42,Y=84
X=38,Y=78
Observe the pattern between 26 and Y. Multiplying 26 by 3 gives 78, which is a common pattern in such numerical analogies (X3 = 114; 263 = 78).
Observe the pattern between 26 and Y. Multiplying 26 by 3 gives 78, which is a common pattern in such numerical analogies (X3 = 114; 263 = 78).
Analyze the right side pair
We are given 26: Y. Testing the multiplier 3: 26 * 3 = 78. This matches the logic for the left side pair: X * 3 = 114.
Determine X
From the equation X * 3 = 114, we solve for X: X = 114 / 3 = 38. Therefore, X = 38.
Confirm the result
Substituting X = 38 and Y = 78 into the expression, we get 38 : 114 :: 26 : 78. Both ratios follow the pattern of multiplying the first number by 3 to obtain the second.
A: 31 * 3 = 93, not 114; B: 39 * 3 = 117, not 114; D: 42 * 3 = 126, not 114.
C is correct because the logic applied to both pairs is multiplying the first number by 3 to reach the second, satisfying 38 * 3 = 114 and 26 * 3 = 78.
When faced with unknown variables on both sides, always test simple arithmetic multipliers or squares/cubes first, as these are the most common patterns in competitive exams.
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