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

It is currently 23 Sep 2018, 21:18

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49331
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

Show Tags

New post 16 Apr 2018, 05:02
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (00:27) correct 26% (00:48) wrong based on 96 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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
G
Joined: 31 Oct 2013
Posts: 578
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

New post 16 Apr 2018, 05:18
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
Intern
avatar
B
Joined: 24 Jan 2013
Posts: 11
GMAT ToolKit User
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

Show Tags

New post 16 Jun 2018, 11:18
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

Hence C answer
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1979
Premium Member CAT Tests
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

Show Tags

New post 18 Jun 2018, 12:35
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

Answer C
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3528
Location: United States (CA)
Re: If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

Show Tags

New post 20 Jun 2018, 17:21
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.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2014
If x^7 < x^6 , which of the following could be the value of x ?  [#permalink]

Show Tags

New post 21 Jun 2018, 01:21

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:

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

Answer: C

To read more about the wavy line: https://gmatclub.com/forum/wavy-line-me ... l#p1727247
_________________








Register for free sessions
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

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-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
Intern
avatar
B
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

New post 22 Jul 2018, 21:29
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
GMAT Club Bot
Re: If x^7 < x^6 , which of the following could be the value of x ? &nbs [#permalink] 22 Jul 2018, 21:29
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.