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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number.
. If the pattern is $ (n-2)^2 $, what are the values of X and Y?
X=10, Y=144
X=8, Y=169
X=10, Y=169
X=12, Y=144
X=10, Y=144
Apply the given rule (n-2)2 to both variables: for X: (X-2)2 = 64 and for Y: (14-2)2 = Y.
Apply the given rule (n-2)2 to both variables: for X: (X-2)2 = 64 and for Y: (14-2)2 = Y.
Solve for X
Given the formula (n-2)2 = result. For X: 64, we have (X-2)2 = 64. Taking the square root of both sides, X-2 = 8. Therefore, X = 8 + 2 = 10.
Solve for Y
For 14: Y, apply the same formula (n-2)2. Here n = 14. So, (14-2)2 = 12┬▓ = 144. Thus, Y = 144.
B: X=8 results in 6┬▓=36, not 64; C: Y=169 requires 13┬▓, but 14-2 is 12; D: X=12 results in 10┬▓=100, not 64.
A is correct because applying the rule (n-2)2 to 10 gives (10тБ╗┬▓)2 = 64, and applying it to 14 gives (14-2)2 = 144.
When a specific mathematical rule is provided in the question, prioritize calculating directly using that rule rather than looking for secondary patterns like prime numbers or digit sums.
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