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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:88::12:Y
X = 14, Y = 132
X = 14, Y = 176
X = 8, Y = 152
X = 8, Y = 132
X = 8, Y = 132
Look for a square number relationship: the second number is (n + 2) squared multiplied by something or a simple multiplier. Here, notice 88 = 8 * 11 and 152 = 8 * 19. Actually, the pattern is: (X + 2) * 8 = Y.
Look for a square number relationship: the second number is (n + 2) squared multiplied by something or a simple multiplier. Here, notice 88 = 8 * 11 and 152 = 8 * 19. Actually, the pattern is: (X + 2) * 8 = Y.
Analyze the Given Pair
The ratio is X : 88 :: 12 : Y. Let's test the option values. For Option D: X=8, Y=132.
Verify Mathematical Relation
For X=8, the first pair is 8 : 88. Relation: 8 ├Ч 11 = 88. For Y=132, the second pair is 12 : 132. Relation: 12 ├Ч 11 = 132.
Confirm Uniformity
Both pairs follow the rule: First Number ├Ч 11 = Second Number. Since 8 ├Ч 11 = 88 and 12 ├Ч 11 = 132, Option D is consistent.
A: 14 * 11 = 154 (not 132), B: 14 * 11 = 154 (not 176), C: 8 * 11 = 88, but 12 * 11 = 132 (not 152).
D is correct because both pairs satisfy the multiplication rule (Number ├Ч 11 = Result), where 8 ├Ч 11 = 88 and 12 ├Ч 11 = 132.
In number analogy questions, always test the simplest common multiplier first before complex square/cube rules.
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