Last visit was: 24 Apr 2024, 02:04 It is currently 24 Apr 2024, 02:04

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?

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 11 May 2014
Status:I don't stop when I'm Tired,I stop when I'm done
Posts: 474
Own Kudos [?]: 38816 [53]
Given Kudos: 220
GPA: 2.81
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29901 [14]
Given Kudos: 799
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2285 [9]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
General Discussion
Intern
Joined: 01 May 2015
Posts: 32
Own Kudos [?]: 136 [8]
Given Kudos: 1
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
6
Kudos
2
Bookmarks
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
Own Kudos [?]: 1 [0]
Given Kudos: 7
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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
Joined: 24 Jun 2016
Posts: 335
Own Kudos [?]: 132 [0]
Given Kudos: 21
GMAT 1: 770 Q60 V60
GPA: 4
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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.

Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6271 [4]
Given Kudos: 1646
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
1
Kudos
3
Bookmarks
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.

Intern
Joined: 13 Jan 2018
Posts: 3
Own Kudos [?]: 13 [0]
Given Kudos: 141
GMAT 1: 760 Q55 V50
GPA: 3.59
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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
Joined: 01 Mar 2019
Posts: 29
Own Kudos [?]: 24 [0]
Given Kudos: 8
Location: United States
Schools: Owen '22 (M\$)
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
[1] Assign Test Values

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

a = 2
b = 3
c = 4

[2] 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
Joined: 26 Jul 2018
Posts: 8
Own Kudos [?]: 6 [0]
Given Kudos: 74
Location: India
Schools: ISB '24
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
Shouldn't the question say a,b,c are integers?
Intern
Joined: 25 Sep 2018
Posts: 40
Own Kudos [?]: 22 [0]
Given Kudos: 61
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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
CEO
Joined: 07 Mar 2019
Posts: 2552
Own Kudos [?]: 1813 [0]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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

GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13386 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
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

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Director
Joined: 04 Jun 2020
Posts: 552
Own Kudos [?]: 67 [0]
Given Kudos: 626
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
BrentGMATPrepNow wrote:
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

Is that a rule that we can "subtract ANY VALUE (such as a) from both sides, the inequality remains valid"? Many thanks in advance
Non-Human User
Joined: 09 Sep 2013
Posts: 32640
Own Kudos [?]: 821 [0]
Given Kudos: 0
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If 0 < a < b < c, which of the following statements must be true? [#permalink]
Moderators:
Math Expert
92893 posts
Senior Moderator - Masters Forum
3137 posts