It is currently 23 Nov 2017, 10:10

### 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 June
Open Detailed Calendar

# a, b, and c are positive, is a > b?

Author Message
TAGS:

### Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 151

Kudos [?]: 392 [0], given: 35

Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
a, b, and c are positive, is a > b? [#permalink]

### Show Tags

14 Dec 2012, 09:28
5
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

53% (01:29) correct 47% (01:41) wrong based on 139 sessions

### HideShow timer Statistics

a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c)
(2) b + c < a
[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Kudos [?]: 392 [0], given: 35

Manager
Joined: 13 Dec 2012
Posts: 194

Kudos [?]: 110 [0], given: 29

Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

14 Dec 2012, 10:10
daviesj wrote:
a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c)
(2) b + c < a

1. a/(b+c) > b/(a+c)
=a(a+c) > b(b+c) This means a > b {sufficient}

2. b+c < a
= b < a-c This means a is still > b despite subtracting c {sufficient}
_________________

Blog: The MBA Journey of an African Doctor

Blog updated: July 27, 2014

Kudos [?]: 110 [0], given: 29

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133122 [2], given: 12415

Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

14 Dec 2012, 10:18
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c). Suppose $$a\leq{b}$$, then the numerator (n1) of LHS (a) is less than or equal to the numerator (n2) of RHS (b) AND the denominator (d1) of LHS (b+c) is more than or equal to the denominator (d2) of RHS (a+c). But if this is the case (if $$n_1\leq{n_2}$$ and $$d_1\geq{d_2}$$), then $$\frac{n_1}{d_1}<\frac{n_2}{d_2}$$. Therefore our assumption was wrong, which means that a>b. Sufficient.

(2) b + c < a. a is greater than b plus some positive number, thus a is greater than b. Sufficient.

_________________

Kudos [?]: 133122 [2], given: 12415

Director
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 866 [0], given: 724

Location: India
GPA: 3.21
Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

17 Dec 2012, 02:10
Bunuel wrote:
a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c). Suppose $$a\leq{b}$$, then the numerator (n1) of LHS (a) is less than or equal to the numerator (n2) of RHS (b) AND the denominator (d1) of LHS (b+c) is more than or equal to the denominator (d2) of RHS (a+c). But if this is the case (if $$n_1\leq{n_2}$$ and $$d_1\geq{d_2}$$), then $$\frac{n_1}{d_1}<\frac{n_2}{d_2}$$. Therefore our assumption was wrong, which means that a>b. Sufficient.

(2) b + c < a. a is greater than b plus some positive number, thus a is greater than b. Sufficient.

Hi Bunuel,

Could please explain why you have assumed $$a\leq{b}$$ and not simply a<b.I guess same reason will apply for denominator as well.
Is it because the Q asked whether a>b and hence we take it as $$a\leq{b}$$.

Had the Question been is a>=b,perhaps we would have assumed a<b only.

If we try solving algebraically from st 1

a.a+a.c> b.b+b.c
a2+ac-b2-bc >0

we end up with a condition

(a-b)(a+b-c)>0

We end up with a condition either a>b or a+b>c.This implies either both terms are negative or both positive.

What do we interpret from this

Thanks
Mridul
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 866 [0], given: 724

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133122 [2], given: 12415

Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

17 Dec 2012, 04:48
2
KUDOS
Expert's post
mridulparashar1 wrote:
Bunuel wrote:
a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c). Suppose $$a\leq{b}$$, then the numerator (n1) of LHS (a) is less than or equal to the numerator (n2) of RHS (b) AND the denominator (d1) of LHS (b+c) is more than or equal to the denominator (d2) of RHS (a+c). But if this is the case (if $$n_1\leq{n_2}$$ and $$d_1\geq{d_2}$$), then $$\frac{n_1}{d_1}<\frac{n_2}{d_2}$$. Therefore our assumption was wrong, which means that a>b. Sufficient.

(2) b + c < a. a is greater than b plus some positive number, thus a is greater than b. Sufficient.

Hi Bunuel,

Could please explain why you have assumed $$a\leq{b}$$ and not simply a<b.I guess same reason will apply for denominator as well.
Is it because the Q asked whether a>b and hence we take it as $$a\leq{b}$$.

Had the Question been is a>=b,perhaps we would have assumed a<b only.

Yes, that's correct.

We are asked whether a>b. Assume that a>b is not true, so assume $$a\leq{b}$$. Now, if after some reasoning based on a/(b+c) > b/(a+c) we'll get that $$a\leq{b}$$ cannot hold true, then we'll get that our assumption ($$a\leq{b}$$) was wrong, thus it must be true that a>b.

mridulparashar1 wrote:
a.a+a.c> b.b+b.c
a2+ac-b2-bc >0

we end up with a condition

(a-b)(a+b-c)>0

We end up with a condition either a>b or a+b>c.This implies either both terms are negative or both positive.

What do we interpret from this

Thanks
Mridul

We can do this way too. The problem with your solution is that you factored a^2+ac-b^2-bc incorrectly: $$a^2+ac-b^2-bc=(a-b)(a+b+c)$$.

So, we'd have: $$\frac{a}{b+c} > \frac{b}{a+c}$$ --> $$a^2+ac>b^2+bc$$ --> $$(a-b)(a+b+c)>0$$ Now, since we are give that a, b, and c are positive, then a+b+c>0, thus a-b>0 --> a>b. Sufficient.

Hope it's clear.
_________________

Kudos [?]: 133122 [2], given: 12415

Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 445 [0], given: 49

Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

29 Apr 2013, 13:06
a, b, and c are positive, is a > b?

(1) a/(b+c) > b/(a+c)
(2) b + c < a

from 1

The inequality boils down to
a(a+c) > b(b+c)
(a^2 +ac) - (b^2+bc) >0 . since the 3 unknown are given as +ve and the only difference between the values inside each of the 2 brackets is the values of a and b therefore a>b

from 2

a-b>c ,since c is +Ve therefore we can re write the ineq as a-b>0 therefore a>b

D

Kudos [?]: 445 [0], given: 49

Non-Human User
Joined: 09 Sep 2013
Posts: 15511

Kudos [?]: 283 [0], given: 0

Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

18 Nov 2014, 04:47
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.
_________________

Kudos [?]: 283 [0], given: 0

Current Student
Joined: 03 Oct 2014
Posts: 143

Kudos [?]: 39 [0], given: 89

Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

13 Jan 2015, 23:53
2
This post was
BOOKMARKED
Statement 1 :- a/(b+c)>b/(a+c)

(a+b+c)/(b+c)>(a+b+c)/(a+c)
1/(b+c)>1/(a+c)
a+c>b+c

As all are positive so its safe to presume a>b

Statement 2 :- b+c<a

As all are positive so its safe to presume a>b

Hence D

Kudos [?]: 39 [0], given: 89

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10169

Kudos [?]: 3536 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

14 Jan 2015, 14:37
Hi All,

This DS question can be dealt with in a variety of ways: Algebra, TESTing VALUES to discover patterns, or Number Properties.

We're told that A, B and C are POSITIVE. We're asked if A > B. This is a YES/NO question.

The "crux" of this question is the "C" and how it effects the relationship between A and B in the given inequalities. We can use Number Properties to get to the correct answer.

Fact 1: (A/B+C) > (B/A+C)

In these two fractions, notice that the only difference is that the "A" and the "B" switch positions. The "C" shows up in each denominator in the same capacity. Since the variables are all POSITIVE, they cannot be 0 or negative, so the C essentially has NO IMPACT on the inequality. Making the C "really small" or "really big" won't impact how A and B relate to one another.

For example...
A = 2
B = 1
C = 1
2/2 > 1/3

and

A = 2
B = 1
C = 100
2/101 > 1/102

....have the same end results. We'll be left with...

A/B > B/A

This also means that A CANNOT equal B (otherwise the two fractions would equal one another).
This only holds true when A > B
The answer to the question is ALWAYS YES

Fact 2: B + C < A

Since B and C are both POSITIVE, A MUST be at least "C" greater than B.
The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3536 [0], given: 173

Director
Joined: 26 Oct 2016
Posts: 690

Kudos [?]: 231 [0], given: 855

Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: a, b, and c are positive, is a > b? [#permalink]

### Show Tags

01 Mar 2017, 17:39
Posting official solution of this problem.
Attachments

official_3.PNG [ 104.9 KiB | Viewed 321 times ]

_________________

Thanks & Regards,
Anaira Mitch

Kudos [?]: 231 [0], given: 855

Re: a, b, and c are positive, is a > b?   [#permalink] 01 Mar 2017, 17:39
Display posts from previous: Sort by