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Intern  Joined: 20 May 2012
Posts: 15
Concentration: General Management, Finance
GRE 1: Q168 V162 GPA: 3.82
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What are the values of x and y that satisfy both the equations?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:29) correct 33% (02:20) wrong based on 159 sessions

### HideShow timer Statistics 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)

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.
Manager  Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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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

##### General Discussion
Manager  B
Joined: 14 Mar 2014
Posts: 145
GMAT 1: 710 Q50 V34 Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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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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¯\_(ツ)_/¯ Veritas Prep GMAT Instructor D
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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2
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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.
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Re: What are the values of x and y that satisfy both the equations?  [#permalink]

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_________________ Re: What are the values of x and y that satisfy both the equations?   [#permalink] 25 Nov 2018, 09:31
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