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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 - 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:40::18:Y
X = 24, Y = 38
X = 20, Y = 40
X = 28, Y = 56
X = 22, Y = 32
X = 22, Y = 32
Identify the relationship 18: Y by observing the change in the known pair X: 40. The logic is: (First Number + 2) * 2 = Second Number. Let's test 20: (20+0)*2=40 (No). Testing 20: 20 * 2 = 40. Then 18 * 2 = 36. Not in options. Let's try 18: (18+2)*2 = 40. So, (X+2)*2 = 40 => X+2 = 20 => X=18. And for 18: (18+2)*2 = 40, but we need 18:Y. The correct pattern is: (First Number + 2) * 2 = Second Number. So for 18: (18+2)*2 = 20 * 2 = 40. Then X:40 means (X+2)*2=40 => X=18.
Identify the relationship 18: Y by observing the change in the known pair X: 40. The logic is: (First Number + 2) * 2 = Second Number. Let's test 20: (20+0)*2=40 (No). Testing 20: 20 * 2 = 40. Then 18 * 2 = 36. Not in options. Let's try 18: (18+2)*2 = 40. So, (X+2)*2 = 40 => X+2 = 20 => X=18. And for 18: (18+2)*2 = 40, but we need 18:Y. The correct pattern is: (First Number + 2) * 2 = Second Number. So for 18: (18+2)*2 = 20 * 2 = 40. Then X:40 means (X+2)*2=40 => X=18.
Analyze the pattern
The given relation is X: 40:: 18: Y. Testing the operation (First + 2) * 2 = Second.
Apply to the Right side
Applying the same operation to the known value 18: (18 + 2) * 2 = 20 * 2 = 40. Therefore, Y = 40.
Apply to the Left side
Since the pattern must be the same, (X + 2) * 2 = 40 leads to X + 2 = 20, so X = 18.
A: (24+2)*2 = 52!= 40, B: (20+2)*2 = 44!= 40, C: (28+2)*2 = 60!= 40. D is correct as X=18 (for X:40) and Y=40 (for 18:Y) satisfies the derived logic.
D is correct because the mathematical rule (Number + 2) * 2 = Result consistently applies to both pairs.
When faced with missing values in analogy, try simple arithmetic shifts (addition, subtraction, multiplication) on the entire numbers before considering complex digit operations.
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