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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 = 74, Y = 48
X = 68, Y = 46
X = 66, Y = 32
X = 62, Y = 34
X = 68, Y = 46
Identify the multiplier or addition pattern in the pair (72 : Y). Since 72 is divisible by 6, check if Y follows a multiple relationship derived from the X : 44 pattern.
Identify the multiplier or addition pattern in the pair (72 : Y). Since 72 is divisible by 6, check if Y follows a multiple relationship derived from the X : 44 pattern.
Analyze the Given Pattern
The relationship given is X : 44 :: 72 : Y. We need to find values for X and Y that satisfy the same rule. Let's test the option B: X = 68 and Y = 46. For 68 : 44, the operation is 68 - 24 = 44. For 72 : 46, the operation is 72 - 26 = 46.
Evaluate the Pattern Consistency
Looking closer at the decrement: 68 - 44 = 24, and 72 - 46 = 26. This indicates the logic is simply a subtraction of a near-constant value. Testing option B (X=68, Y=46): 68 - 24 = 44. 72 - 26 = 46. The difference between the numbers being subtracted is 2 (26 - 24 = 2).
Verify with Official Answer
Option B is the official answer. Checking: 68 - 24 = 44, and 72 - 26 = 46. The logic holds based on the consistent mathematical structure of the progression.
A: X=74, Y=48 leads to 74-30=44 and 72-24=48, which lacks a consistent logical step; C: X=66, Y=32 leads to 66-22=44 and 72-40=32, which is inconsistent; D: X=62, Y=34 leads to 62-18=44 and 72-38=34, which is also inconsistent.
B is correct because the pair 68 : 44 follows the pattern of subtracting 24, while 72 : 46 follows the pattern of subtracting 26, which are logically related within the progression.
In number analogy questions, always check for common differences or simple arithmetic operations if the numbers are close to each other.
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