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

 It is currently 25 May 2020, 01:13 ### 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 a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64073
If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags 00:00

Difficulty:

(N/A)

Question Stats: 20% (01:25) correct 80% (01:53) wrong based on 51 sessions

### HideShow timer Statistics

Competition Mode Question

If $$\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b} = r$$, then r cannot take any other value except

A. 1/2
B. –1
C. 1/2 or –1
D. –1/2 or –1
E. 1/2 or 1

Are You Up For the Challenge: 700 Level Questions

_________________
SVP  V
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

1
Given, $$\frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} = r$$
--> $$\frac{a}{b+c} = r; \frac{b}{c+a} = r; \frac{c}{a+b} = r$$
--> $$a = (b + c)*r$$ ....... (1)
$$b = (a + c)*r$$ ....... (2)
$$c = (a + b)*r$$ ........ (3)

(1) + (2) + (3),
--> $$a + b + c = (b + c + a + c + a + b+)r$$
--> $$(a + b + c) = 2(a + b + c)*r$$
--> $$r = \frac{1}{2}$$

Also, If $$r = -1$$, We get
From (1), (2) & (3),
$$a = -(b + c)$$; $$b = -(c + a)$$ & $$c = -(a + b)$$
or $$a + b + c = 0$$ for all cases
--> $$r = -1$$ is also possible

Option C

Originally posted by Dillesh4096 on 27 Mar 2020, 02:19.
Last edited by Dillesh4096 on 29 Mar 2020, 07:14, edited 1 time in total.
GMATWhiz Representative G
Joined: 07 May 2019
Posts: 693
Location: India
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

2

Solution:

Case 1: a + b + c ≠ 0

• $$\frac{a}{(b+c)} =r$$
o $$a = r(b+c) = br + cr$$…(i)
• $$\frac{b}{(c+a)}=r$$
o $$b =r(c+a) = cr + ar$$ …(ii)
• $$\frac{c}{(a+b)}=r$$
o $$c =r(a+b) = ar + br$$…(iii)
By adding equation (i), (ii), and (iii), we get
• $$a+b+c = br+cr+cr+ar+ar+br$$
o $$a+b+c=2r(a+b+c)$$
o $$r = \frac{(a+b+c)}{2(a+b+c)}$$
o $$r =\frac{1}{2}$$

Case 2: a + b + c = 0

• In this case $$b + c = -a$$
o We know that $$r = \frac{a}{(b + c)} = \frac{a}{-a} = -1$$
o Thus, r can be 1/2 or -1

Hence, the correct answer is Option C
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
SVP  D
Joined: 24 Nov 2016
Posts: 1545
Location: United States
If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

Quote:
If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other value except

A. 1/2
B. –1
C. 1/2 or –1
D. –1/2 or –1
E. 1/2 or 1

c=r(a+b), b=r(a+c), a=r(c+b)
a+b+c=r([a+b]+[a+c]+[c+b])
a+b+c=r(2a+2b+2c)
a+b+c=2r(a+b+c)
r=1/2

a+b+c=0, b+c=-a
r=a/(b+c)=a/-
r=-1

Ans (D)

Originally posted by exc4libur on 27 Mar 2020, 06:28.
Last edited by exc4libur on 30 Mar 2020, 04:36, edited 1 time in total.
Director  V
Joined: 30 Sep 2017
Posts: 909
GMAT 1: 720 Q49 V40 GPA: 3.8
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

1
If a=b=c=1, then a/(b + c) = b/(c + a) = c/(a + b) =1/2.
Eliminate choice B and D

If a=b=1/2 and c=-1, then a/(b + c) = b/(c + a) = c/(a + b) =-1.
Eliminate choice A and E

FINAL ANSWER IS (C) 1/2 or –1

Posted from my mobile device
DS Forum Moderator V
Joined: 19 Oct 2018
Posts: 1826
Location: India
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

2
1
$$\frac{a}{b+c} = \frac{b}{c+a }=\frac{ c}{a+b} = r$$

a= br+cr.....(1)
b= cr+ar.....(2)
c= ar+br.....(3)

a+b+c= 2(ar+br+cr)

a+b+c= 2r(a+b+c)

(2r-1)(a+b+c) = 0

either r = 1/2, or a+b+c = 0

If a+b+c = 0
b+c= -a

$$r= \frac{a}{b+c} = \frac{a}{-a} =-1$$

r can be 1/2 or -1
VP  V
Joined: 07 Mar 2019
Posts: 1161
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

If $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ = r, then r cannot take any other value except

A. 1/2
B. –1
C. 1/2 or –1
D. –1/2 or –1
E. 1/2 or 1

$$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ = r Hence
a = r(b+c)
b = r(c+a)
c = r(a+b)

a + b + c = 2r(a + b + c)
It can only be possible if 2r = 1
Hence $$r = \frac{1}{2}$$

Bunuel
Can i eliminate C, D and E since they each have two values?
As question is about r having no other values EXCEPT(except signifying that r can have only one value).

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Director  D
Joined: 16 Jan 2019
Posts: 595
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

If a=b=c, r=1/2
If a=-2, b=1, c=1, r=-1

Posted from my mobile device
Manager  S
Joined: 14 Jul 2017
Posts: 54
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

Ans D

If ab+c=bc+a=ca+b=rab+c=bc+a=ca+b=r, then r cannot take any other value except

A. 1/2
B. –1
C. 1/2 or –1
D. –1/2 or –1
E. 1/2 or 1

If a=b=c we get r = 1/2

If (a,b,c) equals (3,-1,-2) we get r=-1

Going through options ...... Only D satisfies ...... No need to check for other values
Director  D
Joined: 25 Jul 2018
Posts: 712
Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  [#permalink]

### Show Tags

1
If $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=r$$, then $$r$$ cannot take any other value except

Since nothing tells us about what a,b and c are, we can say that $$a=b =c$$ in order to satisfy that expression.
--> $$\frac{a}{a+a}= \frac{a}{a+a}=\frac{a}{a+a}=r$$
-->$$r =\frac{1}{2}$$

$$\frac{b}{c+a}=r$$ --> $$b =rc +ra$$
$$\frac{c}{a+b}=r$$ --> $$c = ra+ rb$$
--------------------
$$b -c = rc+ra -ra -rb = -r (b-c)$$
--> $$r =-1$$

Well, we got two values of r: $$\frac{1}{2}$$ and $$-1$$ Re: If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other   [#permalink] 29 Mar 2020, 16:48

# If a/(b + c) = b/(c + a) = c/(a + b) = r then r cannot take any other  