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If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 07:32
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Competition Mode Question If the operation ? is defined by \(x?y = y\sqrt{x}\) for all positive integers x and y, then \(9?(16?25) =\) A. 60 B. 180 C. 240 D. 300 E. 1200
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 07:44
x?y = y\(\sqrt{x}\) 9?(16?25) Parenthesis first: 9?(25\(\sqrt{16}\)) => 9?(25*4) => 9?(100) => 100\(\sqrt{9}\) => 100*3 = 300 The answer is D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 07:53
x?y=y(x)^(1/2) 9?(16?25) = 9?(25*4) = 100*3 = 300 Answer is therefore D.
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:15
Given: The operation ? is defined by x?y=y√x for all positive integers x and y, Asked: 9?(16?25)= 16?25 = 25√16 = 25*4 =100 9?100 = 100√9 = 100*3 = 300 IMO D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:20
Given: x?y = y(x)^1/2 9?(16?25) 9?(25(16)^1/2) 9?(25*4) 9?(100) 100(9)^1/2 100*3 300 ans is D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:24
9?(16?25)= =\(9?(25 \sqrt{16})\) =\(9? (25*4)\) =\(9?100\) =\(100\sqrt{9}\) =100*3 300 ANSWER
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:25
The operation ? is defined by x?y=y√x for all positive integers x and y, then 9?(16?25)=? first lets solve 16?25=25√16=25*4=100 9?100=100√9=100*3=300......OPTION D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:26
If the operation ? is defined by \(x?y = y\sqrt{x}\) for all positive integers x and y, then \(9?(16?25) =\) 16?25= 25xsquare root of 16 =25x4 =100 Then 9?100= 100xsquare root of 9 = 300 Answer D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 08:29
Let's take care of the first expression 16?25=25 \(\sqrt{16}\)=25*4=100. Now, we have 9?100 or 100\(\sqrt{9}\)=100*3=300 (D)



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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Updated on: 19 Aug 2019, 09:07
Let us tackle the parentheses first: (16?25) = 25 × \(16^{1/2}\) = 25 × 4 = 100
Next: 9?100 = 100 × \(9^{1/2}\) = 100 × 3 = 300
The answer is D
Originally posted by bebs on 19 Aug 2019, 08:57.
Last edited by bebs on 19 Aug 2019, 09:07, edited 1 time in total.



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 09:24
If the operation ? is defined by x?y = yx^(1/2) for all positive 25 integers x and y, then 9?(16?25)= 16?25 gives 25 x squre root of 16 = 100 now 9?100 gives 100 x square root of 9 = 300 hence ans D is correct choice
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 09:28
9?(16?25)=9?(25*sqrt 16)=9?(25*4)=9?100=100*sqrt 9=100*3=300



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 09:49
9?(16?25) equates to 9?(x?y) where x = 16 and y = 25 9?(y√x) 9?(25√16) 9? (25x4) 9?100 100√9 100x3 300 Answer(D)
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 09:52
If the operation ? is defined by x?y=y√x for all positive integers x and y, then 9?(16?25)
Given : x?y=y√x (only for positive integers)
To Find : 9?(16?25)
Solution : Lets take Z= (16?25) first. Lets say, X=16 and Y=25
Now we know that x?y=y√x So, (16?25) = 25√16 => 25*4 => 100 Now we have Z=100 and we are left with 9?(Z), (Z=100) so now, X=9, Y=100 9?(100) = 100√9 = 100*3 = 300
IMO
D. 300



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 09:54
This is a fairly simple question, so let's jump into it. according to question x?y = y(x)^1/2 9?(16?25) > Let's start with the brackets
16?25 = 25*(16)^1/2= 100 So question now simplifies to 9?100 100*(9)^1/2 = 100*3 = 300 [D]



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 10:05
If the operation ? is defined by x?y=yx√x?y=yx for all positive integers x and y, then 9?(16?25)=9?(16?25)=
A. 60
B. 180
C. 240
D. 300
E. 1200
expression can be solve ; 25√16; 100 9?100 ' 100 √9 ; 300 IMO D



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 10:23
If the operation ? is defined by x?y=y√x for all positive integers x and y, then 9?(16?25)= A. 60 B. 180 C. 240 D. 300 E. 1200 9?(16?25)=9?(25 * 16^1/2)=9?(25*4)=9?100=100*9^1/2=100*3=300
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 10:44
Given: x?y=yx^1/2
9?(16?25)
Lets start from parenthesis 16?25 compare it with definition of ?. our x is 16 and y is 25. so, 16?25 = 25 * 16 ^1/2 = 100 Now coming to 9?100 , again x=9 and Y= 100 9?100= 100* 9^1/2 = 100*3 = 300
And choice D



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 10:48
16?25 = 25 * \sqrt{16} = 25 * 4 =100
Again,
9?100 = 100 *\sqrt{9} = 100 * 3 = 300 (D)



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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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19 Aug 2019, 11:16
9?(16?25) works out to be 25root16 which is 100. 9?100 is 100root9 which works out to be 300. IMO D
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive
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