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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:163::74:Y
X = 81, Y = 149
X = 93, Y = 156
X = 86, Y = 129
X = 79, Y = 145
X = 81, Y = 149
Look for the relationship between the two known numbers: 163 and 74. Since 163 - 89 = 74, check if the same logic applies to the options, or check if the operation involves doubling or squaring. Actually, observe the transformation: (163-1) / 2 = 81. Therefore, for 74, (74-1)/2 does not yield an integer. Let's re-evaluate: Maybe 74 is derived from X via (X-C)/2 or (X+C)/2. Actually, the pattern is: (X + 25) / 2 = 74 => X + 25 = 148 => X = 123 (No). Let's check 163 and 74: 163 - 74 = 89. 89 is a prime number. Let's look at the options: 81, 93, 86, 79. The most common pattern in these types of questions is X * 2 - k = 163 or similar. Let's check Option A: (81 * 2) + 1 = 163 and (74 * 2) + 1 = 149. This fits perfectly!
Look for the relationship between the two known numbers: 163 and 74. Since 163 - 89 = 74, check if the same logic applies to the options, or check if the operation involves doubling or squaring. Actually, observe the transformation: (163-1) / 2 = 81. Therefore, for 74, (74-1)/2 does not yield an integer. Let's re-evaluate: Maybe 74 is derived from X via (X-C)/2 or (X+C)/2. Actually, the pattern is: (X + 25) / 2 = 74 => X + 25 = 148 => X = 123 (No). Let's check 163 and 74: 163 - 74 = 89. 89 is a prime number. Let's look at the options: 81, 93, 86, 79. The most common pattern in these types of questions is X * 2 - k = 163 or similar. Let's check Option A: (81 * 2) + 1 = 163 and (74 * 2) + 1 = 149. This fits perfectly!
Analyze the pattern
We test the relationship (Number * 2) + 1. For 81: 81 * 2 + 1 = 162 + 1 = 163. This matches the first pair X:163.
Apply to second pair
Using the same logic for the second pair 74:Y, we calculate 74 * 2 + 1 = 148 + 1 = 149.
Match with options
The result X=81, Y=149 matches Option A.
B: 932+1=187 (not 163), C: 862+1=173 (not 163), D: 79*2+1=159 (not 163).
A is correct because the pattern follows (Number * 2) + 1 for both pairs (81 * 2 + 1 = 163 and 74 * 2 + 1 = 149).
In number analogy questions, always test basic arithmetic operations (+, -, *, /) and squares/cubes before moving to complex digit-based operations.
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