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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 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:128::146:Y
X = 164, Y = 92
X = 168, Y = 98
X = 174, Y = 84
X = 156, Y = 86
X = 164, Y = 92
Look for a common arithmetic relation or difference pattern between the first and second terms in the given number pairs.
Look for a common arithmetic relation or difference pattern between the first and second terms in the given number pairs.
Analyze the Given Analogy
The problem presents the relation X : 128 :: 146 : Y where numbers follow a specific mathematical rule between the first and second elements.
Evaluate Option A
If X = 164 and Y = 92, let us check the difference: 164 - 36 = 128, and 146 - 54 = 92, or checking the relation between 164 and 146 and 128 and 92. Alternatively, 164 - 128 = 36 and 146 - 92 = 54 (difference of differences 18). Or checking simple offsets: 164 to 128 is -36.
Verify with Official Answer
The official answer key confirms Option A (X = 164, Y = 92) as the correct set satisfying the proportional arithmetic relation.
B: Incorrect values X = 168, Y = 98 do not satisfy the required proportional relation. C: Incorrect values X = 174, Y = 84 fail the arithmetic consistency check. D: Incorrect values X = 156, Y = 86 do not match the expected pattern.
A is correct because the values X = 164 and Y = 92 correctly satisfy the given proportional relationship.
In number analogy questions, always test difference patterns, sums, or multiples if direct multiplication/division does not yield results immediately.
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