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04 Apr 2017, 08:45
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A
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Difficulty:
65%
(hard)
Question Stats:
65% (02:40) correct
35%
(02:58)
wrong
based on 368
sessions
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In a certain sequence, termn = 2(termn-1)\(^n\)
If (term6)/(term5) = \(4^8\), what is the value of term4 ?
A) \(2^{0.4}\)
B) \(2^{0.5}\)
C) \(2^{0.75}\)
D) \(2^{0.8}\)
E) \(2^{1.25}\)
*kudos for all correct solutions
If (term6)/(term5) = \(4^8\), what is the value of term4 ?
A) \(2^{0.4}\)
B) \(2^{0.5}\)
C) \(2^{0.75}\)
D) \(2^{0.8}\)
E) \(2^{1.25}\)
*kudos for all correct solutions
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Updated on: 28 May 2020, 09:30
Originally posted by BrentGMATPrepNow on 05 Apr 2017, 07:27.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:30, edited 1 time in total.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:30, edited 1 time in total.
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GMATPrepNow
Let k = term4 [this will make our calculations much easier to follow]
term5 = 2(term4)\(^5\)
= \(2k^5\)
term6 = 2(term5)\(^6\)
= \(2(2k^5)\)\(^6\)
= \((2)(2^6)(k^{30})\)
= \((2^7)(k^{30})\)
So, (term6)/(term5) = \(\frac{(2^7)(k^{30})}{(2k^5)}\)
= \(2^6k^{25}\)
Since we're told that (term6)/(term5) = \(4^8\), we can write the following...
\(2^6k^{25} = 4^8\)
\(2^6k^{25} = (2^2)\)\(^8\)
\(2^6k^{25} = 2^{16}\)
Divide both sides by \(2^6\) to get: \(k^{25} = 2^{10}\)
Raise both sides to the power of 1/25 to get: \((k^{25})\)\(^{1/25}\) = \((2^{10})\)\(^{1/25}\)
Simplify: \(k = 2^{10/25}\)
Simplify: \(k = 2^{0.4}\)
Answer: A
General Discussion
04 Apr 2017, 09:04
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(term6)/(term5) = 4^8, can be written as
[2 * (term5)^6]/[2 * (term4)^5] = 2^16, this can be further simplified to
[(2* (term4)^5)^6]/[(term4)^5] = 2^16, this can be further simplified to
[(2^6) * (term4^30)] /[(term4)^5] = 2^16, this can be further simplified to
term4^25 = 2^10 ==> term4 = 2 ^ (10/25) ==> term4 = 2^0.4
Answer is A) 2^0.4
[2 * (term5)^6]/[2 * (term4)^5] = 2^16, this can be further simplified to
[(2* (term4)^5)^6]/[(term4)^5] = 2^16, this can be further simplified to
[(2^6) * (term4^30)] /[(term4)^5] = 2^16, this can be further simplified to
term4^25 = 2^10 ==> term4 = 2 ^ (10/25) ==> term4 = 2^0.4
Answer is A) 2^0.4
