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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:59::20:Y
X = 15, Y = 80
X = 16, Y = 80
X = 16, Y = 79
X = 15, Y = 79
X = 15, Y = 79
The pattern is 4 * N = M + 1, where N is the first number and M is the second (or 4N - 1 = M). Testing X:59 and 20:Y, we find 20*4 - 1 = 79, so Y=79. Solving for X: 4X - 1 = 59 implies 4X = 60, so X = 15.
The pattern is 4 * N = M + 1, where N is the first number and M is the second (or 4N - 1 = M). Testing X:59 and 20:Y, we find 20*4 - 1 = 79, so Y=79. Solving for X: 4X - 1 = 59 implies 4X = 60, so X = 15.
Analyze the pattern
Observe the relationship in the complete pair 20: Y. Applying the operation (N * 4) - 1 to 20: (20 * 4) - 1 = 80 - 1 = 79. Thus, Y = 79.
Solve for X
Apply the same inverse logic to the first pair X: 59: (X * 4) - 1 = 59. Adding 1 to both sides gives 4X = 60. Dividing by 4 gives X = 15.
A: Incorrect because X=15 is correct, but Y=80 is wrong (it should be 79). B: Incorrect because X=16 is wrong (16*4-1=63). C: Incorrect because X=16 is wrong.
D is correct because the mathematical relationship is (Number * 4) - 1, which results in X=15 and Y=79.
In analogy questions with numbers, always check if the operations involve simple multiplication/division followed by addition/subtraction. If the pattern is complex, look for square or cube relations (e.g., n┬▓ +/- k).
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