If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?

Question

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/

sterling19 · Accepted Answer

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.

PareshGmat · Answer

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

onamarif · Answer

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}

ameyaprabhu · Answer

Hi,

Is it wrong to consider k^5/4 as K^1? (can we do numerator - denominator for the exponents?)

mikemcgarry · Answer

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 Questions Mike :-)

TimeTraveller · Answer

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.

ameyaprabhu · Answer

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)

TimeTraveller · Answer

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.

mrinal0308 · Answer

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 =================================

Timebomb · Answer

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

ScottTargetTestPrep · Answer

Solution:

We can create the equation:

K^(3/2) = 1.5K^(5/4)

Multiplying both sides by 2, we have:

2K^(3/2) = 3K^(5/4)

Raising both sides to the 4th power, we have:

16K^6 = 81K^5

K^6/K^5 = 81/16

K = 81/16

Answer: E

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If K^(3/2) is 50% bigger than k^(5/4), what is the value of K?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards