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What are the values of x and y that satisfy both the equations?

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What are the values of x and y that satisfy both the equations?  [#permalink]

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New post Updated on: 03 Aug 2015, 12:25
3
10
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

71% (01:53) correct 29% (02:05) wrong based on 123 sessions

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What are the values of x and y that satisfy both the equations?

2^(0.7x) × 3^(−1. 25y) = (8√6)/27

4^(0.3x) × 9^(0.2y) = 8 × (81)^1/5

(a) x = 2, y = 5
(b) x = 2.5, y = 6
(c) x = 3, y = 5
(d) x = 3, y = 4
(e) x = 5, y = 2


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Source: Gmat Cat By Nill (Peterson)

Originally posted by GMATnavigator on 03 Aug 2015, 10:29.
Last edited by Bunuel on 03 Aug 2015, 12:25, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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New post 03 Aug 2015, 12:52
1
GMATnavigator wrote:
What are the values of x and y that satisfy both the equations?

2^(0.7x) × 3^(−1. 25y) = (8√6)/27

4^(0.3x) × 9^(0.2y) = 8 × (81)^1/5

(a) x = 2, y = 5
(b) x = 2.5, y = 6
(c) x = 3, y = 5
(d) x = 3, y = 4
(e) x = 5, y = 2

Source: Gmat Cat By Nill (Peterson)


2^(0.7x) × 3^(−1. 25y) = (8√6)/27
= 2^(7x/10) * 1/(3^{5y/4}) = \(\frac{(2^3 * √2 * √3 )}{3^3}\)
= 2^(7x/10) * 1/(3^{5y/4}) = \(\frac{(2^3 * √2 )}{3^2 *√3}\)
= 2^(7x/10) * 1/(3^{5y/4}) = \(\frac{(2^3 * √2 )}{3^(2.5)}\)

Thus 5y/4 = 2.5 --> y = 2. Thus it can only be Option E
We need to solve the 2nd equation as only one of the options contains y=2
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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New post 03 Aug 2015, 13:10
3
1
GMATnavigator wrote:
What are the values of x and y that satisfy both the equations?

2^(0.7x) × 3^(−1. 25y) = (8√6)/27

4^(0.3x) × 9^(0.2y) = 8 × (81)^1/5

(a) x = 2, y = 5
(b) x = 2.5, y = 6
(c) x = 3, y = 5
(d) x = 3, y = 4
(e) x = 5, y = 2


Give Kudos if you like this question :)


Source: Gmat Cat By Nill (Peterson)



\(2^{0.7x} × 3^{−1. 25y} = (8√6)/27\)

=> \(2^{0.7x} × 3^{−1. 25y}= 2^3*2^{1/2}*3^{1/2}*3^{-3}\)

=> \(2^{0.7x} × 3^{−1. 25y}= 2^{7/2}*3^{-5/2}\)

=>0.7x = 7/2 => x = 5.

Only E has option for x = 5

Hence answer is E
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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New post 03 Aug 2015, 20:47
2
1
GMATnavigator wrote:
What are the values of x and y that satisfy both the equations?

2^(0.7x) × 3^(−1. 25y) = (8√6)/27

4^(0.3x) × 9^(0.2y) = 8 × (81)^1/5

(a) x = 2, y = 5
(b) x = 2.5, y = 6
(c) x = 3, y = 5
(d) x = 3, y = 4
(e) x = 5, y = 2


Give Kudos if you like this question :)


Source: Gmat Cat By Nill (Peterson)


This question is an example of how the question can look complicated but be very simple. The options have mostly integral values so finding the answer will be relatively simple.

Focus on the right hand side of first equation.
\(\frac{8\sqrt{6}}{27} = \frac{2^3 * \sqrt{2} * \sqrt{3}}{3^3} = \frac{2^{7/2} *\sqrt{3}}{3^3}\)

So the power of 2 should be 7/2. On the left hand side, 2 is raised to the power 0.7x
0.7x = 7/2
x = 5
If you must verify, put y = 2 and see that it satisfies the equation.
Answer (E)
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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New post 04 Oct 2017, 12:04
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Re: What are the values of x and y that satisfy both the equations? &nbs [#permalink] 04 Oct 2017, 12:04
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