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# For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val

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Math Expert
Joined: 02 Sep 2009
Posts: 58367
For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val  [#permalink]

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12 Mar 2018, 21:41
00:00

Difficulty:

35% (medium)

Question Stats:

66% (00:58) correct 34% (01:18) wrong based on 74 sessions

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For all values x and y, $$x?y = \frac{3^{(2x + 2y)}}{3^{(2x - 2y)}}$$. What is the value of a?b?

(1) a = 2
(2) b = 4

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Math Expert
Joined: 02 Sep 2009
Posts: 58367
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val  [#permalink]

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12 Mar 2018, 21:44
Intern
Joined: 18 Jul 2016
Posts: 35
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val  [#permalink]

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12 Mar 2018, 22:28
2
1
$$x?y =\frac{3^{(2x + 2y)}}{3^{(2x – 2y)}}$$

=>$$x?y =3^{(2x + 2y) -(2x – 2y)}$$ -- as $$\frac{a^m}{a^n} = a^{m-n}$$

=>$$x?y =3^{4y}$$

Hence, for $$a?b$$, value of b is sufficient to answer

statement 1 : a = 2 ;not sufficient

statement 2 : b = 4; sufficient

IMO - B
Manager
Joined: 01 Feb 2017
Posts: 243
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val  [#permalink]

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13 Mar 2018, 11:53
3^2(a+b) = 9^a * 9^b
3^2(a-b) = 9^a / 9^b

Dividing above, we get the expression:
9^b * 9^b = 81^b

So, we just need value of b to solve the expression.

Therefore, Ans B

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Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val   [#permalink] 13 Mar 2018, 11:53
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