It is currently 23 Feb 2018, 04:47

### 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 certain box contains only blue (b), green (g) and red(r)

Author Message
TAGS:

### Hide Tags

Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 89
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

26 May 2013, 09:45
4
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:26) correct 34% (01:33) wrong based on 441 sessions

### HideShow timer Statistics

A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1)$$\frac{b}{(g+r)}>\frac{r}{(g+b)}$$

(2) g > b
[Reveal] Spoiler: OA

_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1121
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

26 May 2013, 10:45
3
KUDOS
3
This post was
BOOKMARKED
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)
Case b=10 g=1 r=1
$$\frac{10}{1+1}>\frac{1}{10+1}$$ in this case the answer is blue
Case b=10 g=20 r=1
$$\frac{10}{20+1}>\frac{1}{10+20}$$ in this case the answer is green
Not sufficient

(2) g > b
Not sufficient

(1+2)
$$b(g+b)>r(g+r)$$
$$bg+b^2>rg+r^2$$
$$b^2-r^2>rg-bg$$
$$(b+r)(b-r)>g(r-b)$$
CASE if $$r>b$$ we have $$r-b>0$$ and $$b-r<0$$
$$(+)(-)>(+)(+)$$
$$(-)>(+)$$ Not possible
CASE if $$b>r$$ we have $$b-r>0$$ and $$r-b<0$$
$$(+)(+)>(+)(-)$$ Possible
So we find out that $$b>r$$ so $$g>b>r$$
C
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Math Expert
Joined: 02 Sep 2009
Posts: 43894
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

26 May 2013, 12:47
atalpanditgmat wrote:
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)

(2) g > b

OA
[Reveal] Spoiler:
after discussion

Similar question to practice from GMAT PREP: a-certain-jar-contains-only-b-black-marbles-w-white-marbles-104924.html
_________________
Manager
Joined: 14 Jan 2013
Posts: 151
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

15 Jan 2014, 15:28
3
KUDOS
2
This post was
BOOKMARKED
atalpanditgmat wrote:
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)

(2) g > b

Using one of the Bunuel Method-

b/g+r +1 > r/g+b+1

= b+g+r/g+r > b+g+r/g+b

= g+b>g+r

=b>r ( not Suff as no clue of g)

2. Not Suff, as no clue of r

1+2 , Suff
_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Current Student
Joined: 25 Sep 2012
Posts: 281
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

17 Mar 2015, 02:57
Zarrolou wrote:
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)
Case b=10 g=1 r=1
$$\frac{10}{1+1}>\frac{1}{10+1}$$ in this case the answer is blue
Case b=10 g=20 r=1
$$\frac{10}{20+1}>\frac{1}{10+20}$$ in this case the answer is green
Not sufficient

(2) g > b
Not sufficient

(1+2)
$$b(g+b)>r(g+r)$$
$$bg+b^2>rg+r^2$$
$$b^2-r^2>rg-bg$$
$$(b+r)(b-r)>g(r-b)$$ --------------- (A)
CASE if $$r>b$$ we have $$r-b>0$$ and $$b-r<0$$
$$(+)(-)>(+)(+)$$
$$(-)>(+)$$ Not possible
CASE if $$b>r$$ we have $$b-r>0$$ and $$r-b<0$$
$$(+)(+)>(+)(-)$$ Possible
So we find out that $$b>r$$ so $$g>b>r$$
C

I reached till (A) but then had no clue and selected (E) as answer. How did could you reason beyond that?
Intern
Joined: 03 Mar 2015
Posts: 3
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

10 May 2015, 08:52
1. b/g+r > r/g+b, add 1 both sides we get

g+b+r/g+r > g+b+r/g+b ----> b>r ..not suff
2. g> b not suff
1 & 2 Suff.
Retired Moderator
Joined: 29 Oct 2013
Posts: 282
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

09 Dec 2015, 11:32
Let b, g and r be fraction of blue, green and red marbles in the box. so b+g+r=1

st1) b/(g+r) > r/(g+b)--> b/(1-b) > r/(1-r) --> (1-b)/b < (1-r)/r --> b>r. INSUF
St2) g > b INSUF

1+2--> g>b>r we know g is most likely to be picked. SUFF Ans:C
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Board of Directors
Joined: 17 Jul 2014
Posts: 2734
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

17 Mar 2016, 17:37
atalpanditgmat wrote:
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1)$$\frac{b}{(g+r)}>\frac{r}{(g+b)}$$

(2) g > b

my approach:
cross multiply:
bg+b^2 > rg + r^2 - subtract r^2 from both sides then subtract bg from both sides
b^2 - r^2 > rg - bg -> factor both sides
(b+r)(b-r) > g(r-b)

note that we work with marbles - these cannot be negative.
we can conclude that r-b is negative, and b>r.
otherwise if b-r is negative, then multiplying it by a positive number would get a negative number. and a positive number (g) when multiplied by a positive number (r-b) will yield a positive number, but in this case the equation given is not true.

from statement 1, we only know that b>r. alone is insufficient.

statement 2 alone is insufficient.

1+2
we are told that b>r, and g>b. so g>b>r. green marbles are the most likely to be picked.
Director
Joined: 04 Jun 2016
Posts: 642
GMAT 1: 750 Q49 V43
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

05 Aug 2016, 03:42
atalpanditgmat wrote:
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1)$$\frac{b}{(g+r)}>\frac{r}{(g+b)}$$

(2) g > b

From stimulus we know that there are only Blue, Green and Red marbles.
So the probability of being picked will be directly proportional to the the number.
If Green has the highest number then green will have the highest probability
If Red has the highest number then red will have the highest probability
If Blue has the highest number then blue will have the highest probability

(1)$$\frac{b}{(g+r)}>\frac{r}{(g+b)}$$
This tells us that ratio of blue to other two colors is higher than ratio of red to other two colors
Meaning that Blue is more in number than Red.
But we don't know the number of green
INSUFFICIENT

(2) g > b[/quote]
This tells us that Green is more than blue
But we do not know anything about Red
INSUFFICIENT

COMBINE
GREEN > BLUE>RED

SUFFICIENT

The probability of green is highest and red is lowest.
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Intern
Joined: 02 Apr 2016
Posts: 2
Re: A certain box contains only blue (b), green (g) and red(r) [#permalink]

### Show Tags

22 Oct 2017, 20:49
Another way to solve:

Let total t = b + g + r

Statement 1:
b/(g + r) > r/(g + b)
=> b/(t - b) > r/(t - r)
=> bt - br > rt - br
=> bt > rt
=> b > r

Not Suff since we don't know about g.

Statement 2:
g > b

Not Suff since we don't know about r.

Statement 1 and 2 together sufficient: g > b > r
=> g is most likely to be selected
Re: A certain box contains only blue (b), green (g) and red(r)   [#permalink] 22 Oct 2017, 20:49
Display posts from previous: Sort by