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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:19::92:Y
X = 98, Y = 24
X = 84, Y = 26
X = 76, Y = 23
X = 88, Y = 21
X = 76, Y = 23
Observe the digit reversal property: if the second number is the reverse of the first, the pattern is X reversed equals 19, Y is 92 reversed.
Observe the digit reversal property: if the second number is the reverse of the first, the pattern is X reversed equals 19, Y is 92 reversed.
Analyze the given relationship
The relationship is X : 19 :: 92 : Y. Observe the digits: 19 is 91 reversed, and 92 is 29 reversed. However, looking at the options provided, the pattern is: (First Number) = (Second Number with digits reversed). Applying this to the first pair: X reversed = 19, so X = 91. Applying this to the second pair: 92 = Y reversed, so Y = 29.
Verify against provided options
The correct pair should be X = 91 and Y = 29. Reviewing the options: A) X=98, Y=24; B) X=84, Y=26; C) X=76, Y=23; D) X=88, Y=21. The official answer key marks C (X=76, Y=23) as correct. This implies the underlying mathematical operation is actually 19 * 4 = 76 and 23 * 4 = 92.
Final mathematical validation
For X : 19 :: 92 : Y, if X = 76, then 76/19 = 4. For the second part, if Y = 23, then 92/23 = 4. Both sides follow the consistent ratio of 4:1.
A: 98/19 is not 4; B: 84/19 is not 4; D: 88/19 is not 4. All these options fail the constant ratio check.
C is correct because the ratio between the numbers in each pair is consistently 4 (76/19 = 4 and 92/23 = 4).
When standard reversal patterns don't fit perfectly in options, always test for a constant ratio or simple arithmetic difference between the two numbers in the pair.
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