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GMATnavigator
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What are the values of x and y that satisfy both the equations?
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 Updated on: 03 Aug 2015, 11:25
Originally posted by GMATnavigator on 03 Aug 2015, 09:29.
Last edited by Bunuel on 03 Aug 2015, 11:25, edited 1 time in total.
Renamed the topic and edited the question.
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45% (medium)

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72% (02:51) correct 28% (02:31) wrong based on 493 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)
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What are the values of x and y that satisfy both the equations?
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03 Aug 2015, 12:10
GMATnavigator
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)
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\(2^{0.7x} × 3^{−1. 25y} = (8√6)/27\)

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

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

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

Only E has option for x = 5

Hence answer is E
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What are the values of x and y that satisfy both the equations?
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03 Aug 2015, 19:47
GMATnavigator
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)
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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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VenoMfTw
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What are the values of x and y that satisfy both the equations?
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03 Aug 2015, 11:52
GMATnavigator
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)
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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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What are the values of x and y that satisfy both the equations?
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