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# If the operation ? is defined by x?y = yx^(1/2) for all positive

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If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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19 Aug 2019, 07:32
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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  [#permalink]

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19 Aug 2019, 07:44
1
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

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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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19 Aug 2019, 07:53
x?y=y(x)^(1/2)
9?(16?25) = 9?(25*4) = 100*3 = 300

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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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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,

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  [#permalink]

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19 Aug 2019, 08:20
1
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  [#permalink]

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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

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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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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  [#permalink]

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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

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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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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  [#permalink]

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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

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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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
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Re: If the operation ? is defined by x?y = yx^(1/2) for all positive  [#permalink]

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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  [#permalink]

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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

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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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   [#permalink] 19 Aug 2019, 11:16

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