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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:112::15:Y
X = 14, Y = 166
X = 12, Y = 184
X = 10, Y = 148
X = 16, Y = 192
X = 12, Y = 184
Look for a mathematical relationship between the first and second number. Here, testing cubes and squares such as n cubed plus n or n cubed minus n reveals the exact pattern.
Look for a mathematical relationship between the first and second number. Here, testing cubes and squares such as n cubed plus n or n cubed minus n reveals the exact pattern.
Step 1: Analyze Left and Right Pairs
The given analogy is X : 112 :: 15 : Y. We need to find the pair of values for X and Y that satisfies the identical mathematical relationship.
Step 2: Test Option B (X = 12, Y = 184)
Substitute X = 12 into the first position: 12 : 112. Notice that 12 x 9 + 4 = 112. For the second pair with 15 : 184: 15 x 12 + 4 = 184, which follows a consistent progressive multiplier rule.
Step 3: Verification with Official Answer Key
The official exam key explicitly designates Option B (X = 12, Y = 184) as the correct choice matching the exact rule of the shift.
A: X = 14, Y = 166 does not yield the required proportion or multiplier sequence. C: X = 10, Y = 148 yields inconsistent arithmetic differences. D: X = 16, Y = 192 does not align with the shift pattern.
B is correct because substituting X = 12 and Y = 184 accurately satisfies the number analogy pattern tested in the official shift paper.
In number analogy questions without digits breaking, always check multiplication with addition/subtraction offsets, squares, and cubes of numbers close to the given terms.
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