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In the following number-pairs, X:30::50:Y. If the pattern is multiplying by 2 and subtracting 10, find X and Y given Y is 90.
20, 90
25, 90
15, 90
30, 90
20, 90
Apply the reverse operation to find X: To find X from 30, reverse the subtraction (add 10) and then the multiplication (divide by 2).
Apply the reverse operation to find X: To find X from 30, reverse the subtraction (add 10) and then the multiplication (divide by 2).
Analyze the pattern
The rule is: (Number * 2) - 10 = Result. Applying this to X: (X * 2) - 10 = 30.
Solve for X
X * 2 = 30 + 10 implies X * 2 = 40, therefore X = 20.
Verify Y given Y is 90
The question defines Y as 90. Checking the pattern: (50 * 2) - 10 = 100 - 10 = 90. This confirms the pattern holds and Y = 90.
B: 25 would result in (25 * 2) - 10 = 40, not 30. C: 15 would result in (15 * 2) - 10 = 20, not 30. D: 30 would result in (30 * 2) - 10 = 50, not 30.
A is correct because applying the inverse operation (30 + 10) / 2 yields X = 20, while the given Y = 90 satisfies the pattern (50 * 2) - 10 = 90.
In number analogy questions, always test the pattern on the given side first to verify the rule before applying inverse operations to the unknown side.