GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 04:14 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 0 < a < b < c, which of the following statements must be true?

Author Message
TAGS:

### Hide Tags

Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 515
GPA: 2.81
If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

1
26 00:00

Difficulty:   5% (low)

Question Stats: 86% (01:10) correct 14% (01:15) wrong based on 1894 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
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4987
GMAT 1: 770 Q49 V46
If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

5
Top Contributor
1
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

Cheers,
Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course. Originally posted by BrentGMATPrepNow on 14 Jun 2016, 14:39.
Last edited by BrentGMATPrepNow on 03 Mar 2018, 14:51, edited 1 time in total.
##### General Discussion
Intern  Joined: 01 May 2015
Posts: 35
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

4
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  Joined: 16 Feb 2016
Posts: 2
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

Hey,

For (1),
0<a<b<c, can't we write it as
a<b....i
a<c...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  S
Joined: 24 Jun 2016
Posts: 344
GMAT 1: 770 Q60 V60
GPA: 4
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

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.

_________________
Stuck in the 600's and want to score 700+ on the GMAT?
If this describes you, we should talk. I specialize in getting motivated students into the 700's.

$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out! http://www.facebook.com/HanoiGMATtutor HanoiGMATTutor@gmail.com Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2800 Re: If 0 < a < b < c, which of the following statements must be true? [#permalink] ### Show Tags 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 _________________ # Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com 250 REVIEWS 5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE NOW WITH GMAT VERBAL (BETA) See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Intern  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 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 Intern  B Joined: 01 Mar 2019 Posts: 34 Location: United States Schools: Owen '22 (M$)
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

 Assign Test Values

Must follow rule: 0 < a < b < c,

a = 2
b = 3
c = 4

 Plug In & Calculate

$$I. 2a > b + c \rightarrow 2(2) > 3 + 4 \rightarrow 4 > 7 \space (FALSE)$$

$$II. c – a > b - a \rightarrow 4 - 2 > 3 - 2 \rightarrow 2 > 1 \space (TRUE)$$

$$III. \frac{c}{a} < \frac{b}{a} \rightarrow \frac{4}{2} < \frac{3}{2} \rightarrow 2 < 1.5 \space (FALSE)$$

Intern  B
Joined: 26 Jul 2018
Posts: 12
Location: India
Schools: ISB'21
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

Shouldn't the question say a,b,c are integers?
Manager  B
Joined: 25 Sep 2018
Posts: 65
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

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

We can let smart numbers
a=2
so,b=3
c=4
Now, we'll apply on each options given☺
And we get option B(||) only matches

Posted from my mobile device
Sloan MIT School Moderator V
Joined: 07 Mar 2019
Posts: 1343
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If 0 < a < b < c, which of the following statements must be true?  [#permalink]

### Show Tags

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
Taking numbers a = 1, b = 2 and c = 3 this is not true

II. c – a > b - a
In 0 < a < b < c, subtracting a from each
0 - a < a - a < b - a < c - a
Hence c - a > b - a True

III. $$\frac{c}{a}$$ < $$\frac{b}{a}$$
As b < c
dividing by 'a' which is positive doesn't impact inequality
Hence $$\frac{b}{a} < \frac{c}{a}$$
not true

_________________ Re: If 0 < a < b < c, which of the following statements must be true?   [#permalink] 04 Mar 2020, 07:12

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