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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 its constituent digits. E.g. 13 тАУ 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: 49:: 17: Y
X = 23, Y = 37
X = 25, Y = 39
X = 21, Y = 37
X = 31, Y = 34
X = 23, Y = 37
Identify the relation as (N - 2) * 2.5 or similar, but here the operation is (N + k) * multiplier; the simplest relation is (X + 2) * 2 = 49 (invalid) or checking squares: (X + 2)2 = 49.
Identify the relation as (N - 2) * 2.5 or similar, but here the operation is (N + k) * multiplier; the simplest relation is (X + 2) * 2 = 49 (invalid) or checking squares: (X + 2)2 = 49.
Analyze the given pattern
Looking at X : 49, we can identify 49 as a perfect square of 7. The pattern follows (Input + 2) squared = Output. Specifically: (X + 2) squared = 49.
Apply logic to X
If (X + 2) squared = 49, then X + 2 = 7, which means X = 5. Checking the options, this does not fit. Let us re-examine: maybe the logic is (X - 2) * something? No, let us check (23 + 2) = 25... wait. Let us check the difference: 49 is 7 squared. 17 is the second number. Let us check the relation (X + 2) squared = 49 is incorrect. Let us test Option A: X=23, Y=37. If X=23, then (23-2) is 21. Not clear. Let us try (X * 2) + 3 = 49 -> 2X = 46 -> X = 23. This works.
Apply the verified operation to the second pair
The operation is (First Number * 2) + 3 = Second Number. For the first pair: (23 * 2) + 3 = 46 + 3 = 49. Applying this to the second pair: (17 * 2) + 3 = 34 + 3 = 37.
B: 252+3=53 not 49, 392+3=81 not 37; C: 212+3=45 not 49, 372+3=77 not 37; D: 312+3=65 not 49, 342+3=71 not 37.
A is correct because the logic (Number * 2) + 3 holds true for both 23 to 49 (232+3=49) and 17 to 37 (172+3=37).
In number analogy questions, always check for simple linear relations (x*a + b) before looking for complex square or cube patterns.
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