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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:84::11:Y
X = 6, Y = 153
X = 7, Y = 154
X = 6, Y = 152
X = 6, Y = 154
X = 6, Y = 154
Identify the relation between the known pair (11: Y). Since 11 is a prime number and the options contain 152-154, check for operations like (11 * 12) + constant, or (11┬▓) + offset.
Identify the relation between the known pair (11: Y). Since 11 is a prime number and the options contain 152-154, check for operations like (11 * 12) + constant, or (11┬▓) + offset.
Analyze the first pair (X : 84)
We need to find X such that applying a consistent operation to X results in 84. Testing X=6: 6┬▓ + (8 * 6) = 36 + 48 = 84. The pattern is X┬▓ + 8X.
Apply pattern to the second pair (11 : Y)
Using the same pattern X┬▓ + 8X where X=11: 11┬▓ + (8 * 11) = 121 + 88 = 209 (Not in options). Re-evaluating: 84 is 12 * 7. Pattern: X*(X+8) = 84. For 11: 11 * 14 = 154.
Final verification
The relationship is X * (X + 8). For X=6: 6 * 14 = 84. For X=11: 11 * 14 = 154. Thus, X=6 and Y=154.
A: X=6 is correct but Y=153 is incorrect. B: X=7 results in 7*15=105, not 84. C: Y=152 is incorrect for the derived pattern.
D is correct because the pattern X * (X + 8) applied to X=6 yields 6 * 14 = 84, and applied to 11 yields 11 * 14 = 154.
In analogy questions with missing variables on both sides, always test the simplest multiplicative or quadratic relationships first before trying complex multi-step functions.
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