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If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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19 Feb 2015, 12:27
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If \(K^{3/2}\) is 50% bigger than \(K^{5/4}\), what is the value of K? (A) \(\frac{\sqrt{3}}{\sqrt{2}}\) (B) \(\frac{3}{2}\) (C) \(\frac{9}{4}\) (D) \(\frac{27}{8}\) (E) \(\frac{81}{16}\) For a set of challenging problems on exponent, as well as the OA to this particular question, see: https://magoosh.com/gmat/2014/challengi ... androots/
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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19 Feb 2015, 14:16
\(K^{3/2} = 1.5 * K^{5/4}\) \(K^{6/4} = {3/2} * K^{5/4}\)
\(\frac{K^{6/4}}{K^{5/4}}\) = \({3/2}\)
\(K ^{1/4} = {3/2}\) \(K = ({3/2})^4\) \(K = {81/16}\)
The correct answer is E.




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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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11 Mar 2015, 22:12
150 is 50% bigger than 100 \(k^{\frac{3}{2}}\) is 50% bigger than \(k^{\frac{5}{4}}\) Setting up the equation: \(k^{\frac{5}{4}} * 150 = 100 * k^{\frac{3}{2}}\) \(k^{\frac{6}{4}  \frac{5}{4}} = \frac{3}{2}\) \(k = (\frac{3}{2})^4 = \frac{81}{16}\) Answer = E
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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02 Jul 2017, 22:11
\(K^\frac{3}{2}\) = \(1.5* K^\frac{5}{4}\) \(K^\frac{3}{2}/K^\frac{5}{4}\) = \(\frac{3}{2}\) \(K^\frac{3}{2}^\frac{5}{4}\) = \(\frac{3}{2}\) \(K^\frac{1}{4}\) =\(\frac{3}{2}\) So, K=\(\frac{81}{16}\)



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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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24 Jul 2017, 09:54
Hi,
Is it wrong to consider k^5/4 as K^1? (can we do numerator  denominator for the exponents?)



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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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24 Jul 2017, 10:13
ameyaprabhu wrote: Hi,
Is it wrong to consider k^5/4 as K^1? (can we do numerator  denominator for the exponents?) Dear ameyaprabhu, I'm happy to respond. My friend, I do not understand your question. Are you asking how to make a fraction appear as an exponent using the LaTex math font? Are you asking what it means to have a fraction in the exponent? I don't know whether you are asking a purely mathematical question or whether you are asking a question about this site. Please clarify. I will also recommend this blog: Asking Excellent QuestionsMike
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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24 Jul 2017, 10:35
mikemcgarry wrote: If \(K^{3/2}\) is 50% bigger than \(K^{5/4}\), what is the value of K? (A) \(\frac{\sqrt{3}}{\sqrt{2}}\) (B) \(\frac{3}{2}\) (C) \(\frac{9}{4}\) (D) \(\frac{27}{8}\) (E) \(\frac{81}{16}\) For a set of challenging problems on exponent, as well as the OA to this particular question, see: https://magoosh.com/gmat/2014/challengi ... androots/\(k^{3/2} = 1.5(k^{5/4})\) \(k^{{\frac{3}{2}}  {\frac{5}{4}}} = 1.5\) \(\frac{3}{2}  \frac{5}{4} = \frac{1210}{8} = \frac{1}{4}\) \(k^{1/4} = 1.5\) \(k = (1.5)^4 = (\frac{3}{2})^4 = \frac{81}{16}\). Ans  E.
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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24 Jul 2017, 17:48
Hi Mike,
While I know K^m/n = nth root of k raised to m, my doubt was more fundamental, in that, I was wondering whether we can simplify the expression do K^(mn). eg. k^5/4 simply becomes K (but doing so doesn't seem to work for this problem and hence I was questioning my basics)



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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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24 Jul 2017, 18:24
ameyaprabhu wrote: Hi Mike,
While I know K^m/n = nth root of k raised to m, my doubt was more fundamental, in that, I was wondering whether we can simplify the expression do K^(mn). eg. k^5/4 simply becomes K (but doing so doesn't seem to work for this problem and hence I was questioning my basics) Hi, Remember the fraction rule: \(\frac{a^{m}}{a^{n}} = a^{mn}\). Here we have \(k^{m}/k^{n}\), where \(m = 3/2\), and \(n = 5/4\), so we get \(k^{mn} = k^{3/2  5/4} = k^{1/4}\). If it was \(k^5/k^4\), that would be equal to \(k^{54} = k^1\). Hope you see the difference.
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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22 Jul 2018, 08:31
mikemcgarry wrote: If \(K^{3/2}\) is 50% bigger than \(K^{5/4}\), what is the value of K? (A) \(\frac{\sqrt{3}}{\sqrt{2}}\) (B) \(\frac{3}{2}\) (C) \(\frac{9}{4}\) (D) \(\frac{27}{8}\) (E) \(\frac{81}{16}\) For a set of challenging problems on exponent, as well as the OA to this particular question, see: https://magoosh.com/gmat/2014/challengi ... androots/The expression is: K^(3/2)=1.5xK^(5/4) Squaring both sides, we get: K^3=(1.5)^2 x K^(5/2) Squaring again, K^6=(1.5)^4 x K^5 Simplifying the powers of K, K= (1.5)^4 that gives, K=81/16 on expanding above as fraction. Answer: E ============ Pls Hit +1 KUDOS if you liked my reply =================================



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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?
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22 Jul 2018, 08:37
E. As k^3/2=1.5*k^5/4 k^6/45/4=1.5 k^1/4=1.5 i.e. 3/2 k= 81/16




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