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18 is related to 162 following a certain logic. Following the same logic, 16 is related to 144. To which of the following is 25 related to following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 тАУ 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.)
215
225
235
245
225
Observe that the second number is the square of half the first number: (N/2)2.
Observe that the second number is the square of half the first number: (N/2)2.
Analyze the first pair (18, 162)
Divide the first number by 2 to get 9. Square the result: 9 * 9 = 81. Multiply 81 by 2 to get 162. Alternatively, the formula is (N/2)2тИЧ2.
Analyze the second pair (16, 144)
Divide 16 by 2 to get 8. Square the result: 8 * 8 = 64. Multiply 64 by 2 to get 128. Wait, looking at the pattern again: (18/2)2тИЧ2= 162 and (16/2)2тИЧ4= 256? No, let's re-verify: 18 * (18/2) = 18 * 9 = 162. 16 * (16/2) = 16 * 8 = 128. Wait, the prompt says 16 is related to 144. 16 * 9 = 144. The multiplier is 9.
Establish the consistent rule
For 18: 18 * (18/2) = 162. For 16: 16 * (16/2 + 1) = 16 * 9 = 144. The multiplier increases by 1 each time? Or simply: (18/2)2тИЧ2= 162. (16/2)2тИЧ2.25 = 144. Let's use: (First number * First number) / 2 = 1818/2 = 162. 1616/2 = 128. That does not fit 144. Let's try: (18/2)2тИЧ2= 162. (16/2)2тИЧ2= 128. Actually, the logic is simply (N/2)2тИЧ2. If 16 relates to 144, it is 16┬▓ / 1.77... No. It is 9 * 16 = 144. 18 * 9 = 162. Both use 9 as a multiplier! 18*(18/2)=162, 16*(16/2+1)=144. Let's re-check 25: 25 * (25/2 + 3.5) = 225. 25 * 9 = 225.
Apply logic to 25
Based on the pattern (First number * 9 = Result), 25 * 9 = 225.
A: 215 is not divisible by 25 and does not fit the multiplier pattern, C: 235 is not divisible by 25 and does not fit the multiplier pattern, D: 245 is not divisible by 25 and does not fit the multiplier pattern.
B is correct because the logic follows multiplying the number by 9 (189=162, 169=144, 25*9=225).
In number analogy questions, if the operation seems complex, check for a common factor or a simple multiplier first.
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