GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Dec 2018, 01:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics

# If x^7 < x^6 , which of the following could be the value of x ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51219
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

16 Apr 2018, 04:02
00:00

Difficulty:

15% (low)

Question Stats:

70% (00:43) correct 30% (00:46) wrong based on 100 sessions

### HideShow timer Statistics

If x^7 < x^6, which of the following could be the value of x?

I. −3
II. 2/3
III. 3/2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

_________________
Director
Joined: 31 Oct 2013
Posts: 883
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

16 Apr 2018, 04:18
1
Bunuel wrote:
If x^7 < x^6, which of the following could be the value of x?

I. −3
II. 2/3
III. 3/2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

This question is designed to test properties of negative numbers and fractions.

1. -3 ...........always true. coz we have the even power.
2. It is also true. proper fraction
3. improper fraction.....while solving this one , reduce the power to verify how this kind of fraction reacts. this violates the given inequality.

thus , the correct answer is C.
Intern
Joined: 24 Jan 2013
Posts: 10
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

16 Jun 2018, 10:18
x^7 < x^6
x^7-x^6<0
x(x^6-1)<0

I. −3
x=-ve, x^6-1 = +ve
overall <-ve, X can be -3

II. 2/3
x=+ve,x^6-1= (2/3)^6-1 , will always be negative
overall -ve, X can be 2/3

III. 3/2
x=+ve, x^6-1+ (3/2)^6-1, will always be positive, cannot be value of X

Hence i and ii ARE CORRECT

Senior SC Moderator
Joined: 22 May 2016
Posts: 2213
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

18 Jun 2018, 11:35
1
1
Bunuel wrote:
If x^7 < x^6, which of the following could be the value of x?

I. −3
II. 2/3
III. 3/2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Number properties often can be verified with testing.

And if questions have numbers with large exponents, usually the question can be replicated on a smaller scale.

We can test values using smaller exponents as long as we stay true to the original problem (inequality).

The prompt gives an inequality that means "a number raised to an odd power is smaller than the number raised to an even power."
Thus: $$x^3 < x^2$$

Which of the following COULD be the value of x?

I. −3
Test: $$(-3)^3=-27$$ and $$(-3)^2=9$$
$$-27<9$$ ... Possible

Number property tested is that
-- A negative number raised to an odd power is negative
-- Raised to an even power, the number is positive

II. 2/3
Test the much easier number $$\frac{1}{2}$$ INSTEAD (any fraction between 0 and 1 works)
$$(\frac{1}{2})^3=\frac{1}{8}$$, and
$$(\frac{1}{2})^2=\frac{1}{4}$$

$$\frac{1}{8}<\frac{1}{4}$$. ...Possible

Property: For any fraction between 0 and 1, the value of the fraction decreases as the exponent increases.

III. 3/2 - Test:
$$(\frac{3}{2})^3=\frac{27}{8}=3.xx$$, and
$$(\frac{3}{2})^2=\frac{9}{4}=2.xx$$

LHS is not < RHS. Not possible

Property: For any number greater than 1, the value of the number increases as the exponent increases

I and II only

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)
Re: If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

20 Jun 2018, 16:21
Bunuel wrote:
If x^7 < x^6, which of the following could be the value of x?

I. −3
II. 2/3
III. 3/2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Since x^7 is less than x^6, x could be either, a positive number between 0 and 1 or a negative number. Thus x could be -3 or 2/3.

Alternate Solution:

Let’s consider each Roman numeral:

If x = -3, then we see that x^7 is a negative number, and x^6 is a positive number. Thus, Roman numeral I works.

If x = 2/3, then x is a proper fraction. For a positive proper fraction, the greater the exponent, the smaller the result. Thus, (2/3 )^7 is less than (2/3 )^6. Roman numeral II works.

If x = 3/2, then (3/2)^7 is greater than (3/2)^6. This outcome would hold for any value of x greater than 1.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2313
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

21 Jun 2018, 00:21

Solution

Given:
• $$x^7 < x^6$$

To find:
• Among the three given values, which is a possible value of x.

Approach and Working:
• $$x^7 < x^6$$
o Subtracting x^6 from both the sides, we get: $$x^6(x-1)<0$$
o We can solve this by the wavy line below:

Hence, for x<1, $$x^6(x-1)<0$$
Hence, the correct answer is option C.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Joined: 07 Aug 2017
Posts: 1
Re: If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

### Show Tags

22 Jul 2018, 20:29
Given: x^7<x^6

Divide both side by x^6
(x^7/x^6)<(x^6/x^6) ..........Since x^6 will always be positive, the sign of inequality doesn't change
x<1

Sincle x<1, only option I(-3) and option II (2/3) is correct. Hence option C
Re: If x^7 < x^6 , which of the following could be the value of x ? &nbs [#permalink] 22 Jul 2018, 20:29
Display posts from previous: Sort by