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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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x and m are positive numbers, and m is a multiple of 3. [#permalink]
Expert's post 00:00

Question Stats: 77% (00:57) correct 22% (01:01) wrong based on 235 sessions
x and m are positive numbers, and m is a multiple of 3.

 Quantity A Quantity B $$\frac{(x^m)}{x^3}$$ $$x^\frac{m}{3}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 8
Page: 331
Difficulty: medium
[Reveal] Spoiler: OA

_________________

Sandy
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Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2970  , given: 394

Re: x and m are positive numbers, and m is a multiple of 3. [#permalink]
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Expert's post
Solution

Since you need to compare $$\frac{x^m}{x^3}=x^(^m ^- ^3 ^)$$with $$x^\frac{m}{3}$$. Since the base in both expressions is the same, a good strategy to use to solve this problem is to plug in numbers for m in both expressions and compare them.

You know that m is a multiple of 3, so the least positive integer you can plug in for m is 3.

If m=3, then $$x^( ^m ^- ^3 ^)=1$$ and x ^$$\frac{m}{3}$$=x. Since x can be any real number, its relationship to 1 cannot be determined from the information given. This example is sufficient to show that the relationship cannot be determined from the information given. The correct answer is Choice D.
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Sandy
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Re: x and m are positive numbers, and m is a multiple of 3. [#permalink]
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We take two multiples of 3. 3 and 6 ond then we solve the given equations once by 3 and then by 6 we will get two different answers. Therefore the answer will be 'D'.
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Re: x and m are positive numbers, and m is a multiple of 3. [#permalink]
sandy wrote:
x and m are positive integers, and m is a multiple of 3.

 Quantity A Quantity B $$\frac{(x^m)}{x^3}$$ x ^ $$(\frac{m}{3})$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 8
Page: 331
Difficulty: medium GRE Instructor Joined: 10 Apr 2015
Posts: 3869
Followers: 157

Kudos [?]: 4628  , given: 70

Re: x and m are positive numbers, and m is a multiple of 3. [#permalink]
1
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Expert's post
sandy wrote:
x and m are positive integers, and m is a multiple of 3.

 Quantity A Quantity B $$\frac{(x^m)}{x^3}$$ $$x^\frac{m}{3}$$

Let's test some possible values

case i: x = 1 and m = 3
We get:
QUANTITY A: $$\frac{(x^m)}{x^3}=\frac{1^3}{1^3}=1$$

QUANTITY B: $$x^\frac{m}{3}=1^\frac{3}{3}=1^1=1$$

In this case, the two quantities are equal

case ii: x = 2 and m = 3
We get:
QUANTITY A: $$\frac{(x^m)}{x^3}=\frac{2^3}{2^3}=1$$

QUANTITY B: $$x^\frac{m}{3}=2^\frac{3}{3}=2^1=2$$

In this case, Quantity B is greater

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: x and m are positive numbers, and m is a multiple of 3.   [#permalink] 04 Apr 2019, 12:15
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