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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 - 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:140.4::38:Y
X = 34, Y = 225.8
X = 23, Y = 240.6
X = 21, Y = 218.4
X = 26, Y = 205.2
X = 26, Y = 205.2
Identify the mathematical relation between the first number (N) and the second number (S) in the given pair 38 : Y. Test standard arithmetic rules such as N ├Ч multiplier + constant or N ├Ч multiplier. Here, 38 ├Ч 5.8 = 220.4, or check options for exact scale.
Identify the mathematical relation between the first number (N) and the second number (S) in the given pair 38 : Y. Test standard arithmetic rules such as N ├Ч multiplier + constant or N ├Ч multiplier. Here, 38 ├Ч 5.8 = 220.4, or check options for exact scale.
Step 1: Understand the Analogy Rule
In number pair analogies of the form A : B :: C : D, the mathematical relationship between A and B must be identical to the relationship between C and D.
Step 2: Test Option D (X = 26, Y = 205.2)
Substitute X = 26 and Y = 205.2 into the equation. For the second pair, 38 ├Ч 5.4 = 205.2. For the first pair, 26 ├Ч 5.4 = 140.4. Both pairs follow the exact same multiplier of 5.4.
A: X = 34 and Y = 225.8 does not maintain the consistent multiplier relation. B: X = 23 and Y = 240.6 gives incorrect products. C: X = 21 and Y = 218.4 fails the uniform ratio test.
Option D is correct because X = 26 and Y = 205.2 both satisfy the identical multiplier relation of multiplying the first number by 5.4 to obtain the second number.
When decimals appear in number analogies, always test simple decimal multipliers (like 1.5, 2.5, 5.4, 7.8) by dividing the second number by the first number.
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