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

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Senior Manager
Joined: 24 Nov 2016
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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, 12:53
Quote:
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

16?25=25√16=25•4=100
9?100=100√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, 14:07
First we should indicate the term in the parenthesis.
X=16,Y=25
25×4=100
9?100 ==>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, 21:44
$$x?y = y\sqrt{x}$$

$$? = \sqrt{x}/x$$

9?(16?25) =

Solve the bracket first.

$$(\sqrt{16}*25)$$ $$= 4*25 = 100$$

$$\sqrt{9}*100 = 3*100 = 300$$

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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, 22:02
If the operation ? is defined by x?y=y√x for all positive integers x and y, then 9?(16?25)=

x?y=y√x
x?y=$$yx^{\frac{1}{2}}$$
?=1/2 - the square root of a positive number

--> 9?(16?25)=$$9^{\frac{1}{2}}(16^{\frac{1}{2}}*25)$$=3*4*25=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, 22:28
Lets not forget about PEMDAS for this question! :O
Although i am pretty sure most of us here will not!

Now, the ones in the Para first -- 16?25 = 25*sqrt16 = 25 * 4 = 100.

Next, it becomes 9?100. Again, 100 * sqrt9 = 100 * 3 = 300.

Hence, D is and should be the answer.
Re: If the operation ? is defined by x?y = yx^(1/2) for all positive   [#permalink] 19 Aug 2019, 22:28

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