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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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Magoosh GMAT Instructor
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If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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19 Feb 2015, 11:27
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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 ... and-roots/

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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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19 Feb 2015, 13:16
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$$K^{3/2} = 1.5 * K^{5/4}$$
$$K^{6/4} = {3/2} * K^{5/4}$$

$$\frac{K^{6/4}}{K^{5/4}}$$ = $${3/2}$$

$$K ^{1/4} = {3/2}$$
$$K = ({3/2})^4$$
$$K = {81/16}$$

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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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11 Mar 2015, 21:12
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150 is 50% bigger than 100

$$k^{\frac{3}{2}}$$ is 50% bigger than $$k^{\frac{5}{4}}$$

Setting up the equation:

$$k^{\frac{5}{4}} * 150 = 100 * k^{\frac{3}{2}}$$

$$k^{\frac{6}{4} - \frac{5}{4}} = \frac{3}{2}$$

$$k = (\frac{3}{2})^4 = \frac{81}{16}$$

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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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02 Jul 2017, 21:11
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$$K^\frac{3}{2}$$ = $$1.5* K^\frac{5}{4}$$
$$K^\frac{3}{2}/K^\frac{5}{4}$$ = $$\frac{3}{2}$$
$$K^\frac{3}{2}-^\frac{5}{4}$$ = $$\frac{3}{2}$$
$$K^\frac{1}{4}$$ =$$\frac{3}{2}$$
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?  [#permalink]

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24 Jul 2017, 08:54
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?  [#permalink]

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24 Jul 2017, 09:13
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:

Mike
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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24 Jul 2017, 09:35
1
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 ... and-roots/

$$k^{3/2} = 1.5(k^{5/4})$$

$$k^{{\frac{3}{2}} - {\frac{5}{4}}} = 1.5$$

$$\frac{3}{2} - \frac{5}{4} = \frac{12-10}{8} = \frac{1}{4}$$

$$k^{1/4} = 1.5$$

$$k = (1.5)^4 = (\frac{3}{2})^4 = \frac{81}{16}$$. Ans - E.
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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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24 Jul 2017, 16:48
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^(m-n). 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?  [#permalink]

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24 Jul 2017, 17:24
1
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^(m-n). 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: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$.

Here we have $$k^{m}/k^{n}$$, where $$m = 3/2$$, and $$n = 5/4$$, so we get $$k^{m-n} = k^{3/2 - 5/4} = k^{1/4}$$. If it was $$k^5/k^4$$, that would be equal to $$k^{5-4} = k^1$$. 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?  [#permalink]

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22 Jul 2018, 07:31
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 ... and-roots/

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.

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Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?  [#permalink]

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22 Jul 2018, 07:37
E.
As k^3/2=1.5*k^5/4
k^6/4-5/4=1.5
k^1/4=1.5 i.e. 3/2
k= 81/16
Re: If K^(3/2) is 50% bigger than k^(5/4), what is the value of K? &nbs [#permalink] 22 Jul 2018, 07:37
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