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

It is currently 24 Sep 2018, 08:33

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 0 < a < b < c, which of the following statements must be true?

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

Hide Tags

Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 542
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 14 Jun 2016, 15:08
1
12
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (00:55) correct 15% (00:46) wrong based on 1039 sessions

HideShow timer Statistics

If 0 < a < b < c, which of the following statements must be true?

I. 2a > b + c
II. c – a > b - a
III. \(\frac{c}{a}\) < \(\frac{b}{a}\)

A) I only
B) II only
C) III only
D) I and II
E) II and III

OG 2017 New Question

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2892
Location: Canada
If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post Updated on: 03 Mar 2018, 15:51
2
Top Contributor
AbdurRakib wrote:
If 0 < a < b < c, which of the following statements must be true?

I. 2a > b + c
II. c – a > b - a
III. \(\frac{c}{a}\) < \(\frac{b}{a}\)

A) I only
B) II only
C) III only
D) I and II
E) II and III

OG 2017 New Question


I. 2a > b + c
Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c.
HOWEVER, if we plug these values into statement I, we see that it is NOT the case that 2a > b + c
So, statement I NEED NOT BE TRUE

II. c – a > b - a
It's already given that c > b
If we subtract ANY VALUE (such as a) from both sides, the inequality remains valid.
So, statement II MUST BE TRUE

III. c/a < b/a
Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c.
HOWEVER, if we plug these values into statement III, we see that it is NOT the case that c/a < b/a
So, statement III NEED NOT BE TRUE

Answer: B

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails


Originally posted by GMATPrepNow on 14 Jun 2016, 15:39.
Last edited by GMATPrepNow on 03 Mar 2018, 15:51, edited 1 time in total.
Intern
Intern
avatar
Joined: 01 May 2015
Posts: 41
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 16 Jun 2016, 05:39
2
I. obvously we cannot say that it "must" be true.

II. c – a > b - a
Cancelling a on both sides
c > b
Definitely true as per question.

III. c/a < b/a
Multiply both sides by "a" (positive)
c < b
Definitely "not" true as per question.

So, only II is correct.
Intern
Intern
avatar
Joined: 16 Feb 2016
Posts: 3
GMAT ToolKit User
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 24 Jun 2016, 14:21
Hey,

For (1),
0<a<b<c, can't we write it as
a<b....i
a<c...ii

adding i and ii

2a<b+c ???? (addition property of inequalities)

Or
Is it like this property holds true only when abcd are different numbers??

Appreciate a clarification!

TIA.
Senior Manager
Senior Manager
User avatar
B
Joined: 24 Jun 2016
Posts: 259
GMAT 1: 770 Q60 V60
GPA: 4
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 26 Jun 2016, 02:31
Nothing indicates what a may be greater than, so I is wrong.
III is always wrong because the order should be reversed.

II is correct.

Answer choice B is correct.
_________________

Offering top quality online and offline GMAT tutoring in SoCal and worldwide.

$80/hour as of May 2018.


http://www.facebook.com/HanoiGMATtutor
HanoiGMATTutor@gmail.com

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 05 Dec 2016, 18:29
1
2
AbdurRakib wrote:
If 0 < a < b < c, which of the following statements must be true?

I. 2a > b + c
II. c – a > b - a
III. \(\frac{c}{a}\) < \(\frac{b}{a}\)

A) I only
B) II only
C) III only
D) I and II
E) II and III


We are given that 0 < a < b < c and need to determine which statements are true. Let’s analyze each Roman numeral.

I. 2a > b + c

2a cannot be greater than the sum of b and c. Since a + a = 2a, a < b, and a < c, a + a < b + c, or 2a < b + c. Statement I is FALSE.

II. c – a > b - a

We can simplify the inequality to c > b. Since we are given that c is greater than b in the stem, c – a is greater than b - a. Statement II is TRUE.

III. c/a < b/a

We can multiply both sides by a and we have c < b (note: we don’t need to switch the inequality sign because a is positive). However, we are given that c is greater than b, so c/a can’t be less than b/a. Statement III is FALSE.

Thus, only Roman numeral II is true.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
B
Joined: 13 Jan 2018
Posts: 5
Location: Canada
GMAT 1: 760 Q55 V50
GPA: 3.59
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

Show Tags

New post 26 Feb 2018, 16:00
A simple and quick approach is to assume values for a, b, c
If a=2, b=3, c=4
I. 2a > b + c = 4 > 7; this is wrong
II. c – a > b - a = 2 > 1; this is correct
III. c/a <b/a = 2 < 1.5; this is wrong

Therefore, II only is correct. Answer is B
GMAT Club Bot
Re: If 0 < a < b < c, which of the following statements must be true? &nbs [#permalink] 26 Feb 2018, 16:00
Display posts from previous: Sort by

If 0 < a < b < c, which of the following statements must be true?

  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®.