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Updated on: 03 Aug 2015, 12:25
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.
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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E
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Difficulty:
45%
(medium)
Question Stats:
73% (02:52) correct
27%
(02:35)
wrong
based on 459
sessions
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Time
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Not Attempted Yet
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)
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)
King407
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Schools: IIMA IIMB IIMC ISB '17 IIM-L '15 INSEAD Jan '17 NUS '18 Kellogg 1YR '17 Booth '16 Tepper '18 McCombs '18
Posts: 68
03 Aug 2015, 13:10
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GMATnavigator
\(2^{0.7x} × 3^{−1. 25y} = (8√6)/27\)
=> \(2^{0.7x} × 3^{−1. 25y}= 2^3*2^{1/2}*3^{1/2}*3^{-3}\)
=> \(2^{0.7x} × 3^{−1. 25y}= 2^{7/2}*3^{-5/2}\)
=>0.7x = 7/2 => x = 5.
Only E has option for x = 5
Hence answer is E
03 Aug 2015, 20:47
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GMATnavigator
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)
