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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Select the option in which the numbers share the same relationship as that shared by the given pairs of numbers. 2 : 16 3 : 81 (NOTE: Operations should be performed on the whole number, 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.)
4 : 256
2 : 32
6 : 216
4 : 64
4 : 256
Identify the exponential relationship: the second number is the first number raised to the power of itself (x: xˣ) or a variant of xⁿ.
Identify the exponential relationship: the second number is the first number raised to the power of itself (x: xˣ) or a variant of xⁿ.
Analyze the given relationship
Given pairs are 2: 16 and 3: 81. The pattern is x: xˣ is not applicable, but rather x: xⁿ where n varies. Specifically, 2⁴ = 16 and 3⁴ = 81. Both follow the pattern x: x⁴.
Evaluate the options based on the x: x⁴ pattern
Checking the options: A) 4: 4⁴ = 4: 256. B) 2: 2⁴ = 16 (not 32). C) 6: 6⁴ = 1296 (not 216). D) 4: 4³ = 64 (not 4⁴).
B: 2⁴ is 16, not 32; C: 6⁴ is 1296, not 216; D: 4³ is 64, which uses a different exponent pattern.
A is correct because the given numbers follow the mathematical pattern x: x⁴, and 4 to the power of 4 equals 256.
When dealing with small numbers in analogies, always check powers, squares, and cubes first before considering basic multiplication or addition.
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