It is currently 22 Sep 2017, 08:28

### 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

# From a bag containing 12 identical blue balls, y identical

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 Jan 2006
Posts: 144

Kudos [?]: 35 [5], given: 0

From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

06 Apr 2006, 15:32
5
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

60% (00:58) correct 40% (01:08) wrong based on 761 sessions

### HideShow timer Statistics

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

A. 17
B. 18
C. 19
D. 20
E. 21
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Sep 2013, 03:54, edited 1 time in total.
Renamed the topic, edited the question, added the answer choices and the OA.

Kudos [?]: 35 [5], given: 0

Manager
Joined: 09 Feb 2006
Posts: 129

Kudos [?]: 8 [0], given: 0

Location: New York, NY

### Show Tags

06 Apr 2006, 15:38
12/x = 2/5

x = 30 total number of balls.

There must be at least 18 yellow balls in the bag.

Kudos [?]: 8 [0], given: 0

Intern
Joined: 02 Jan 2006
Posts: 4

Kudos [?]: 1 [1], given: 0

Location: Bay Area

### Show Tags

07 Apr 2006, 08:18
1
KUDOS
Agree with NTLancer.

Since the prob of blue balls is LESS than 2/5, you need at least 19 yellow balls in the bag.

Kudos [?]: 1 [1], given: 0

Manager
Joined: 27 Mar 2006
Posts: 136

Kudos [?]: 2 [0], given: 0

### Show Tags

07 Apr 2006, 16:54
Agree

The number of yellow balls is atleast 19.

Since yellow balls must be greater than 18...hence least number is 19

Kudos [?]: 2 [0], given: 0

Manager
Joined: 21 Dec 2005
Posts: 102

Kudos [?]: 4 [0], given: 0

### Show Tags

07 Apr 2006, 23:19
Agree with 19 too.

Since 2/5=12/x, x = 30 so if probability is less than 2/5 that means x is >30, say 31 then 31-12=19 yellow balls.

Kudos [?]: 4 [0], given: 0

Intern
Joined: 12 Feb 2006
Posts: 26

Kudos [?]: 12 [0], given: 0

### Show Tags

09 Apr 2006, 12:38
(12 blue) / (12 blue + x yellow) = 2/5

12/30 = 2/5

The denominator must be 30. You have 12 already which means you need 18 yellow balls. This makes the equation equal to each other. However, you want less than 2/5 so add one ball to make it 19.

Kudos [?]: 12 [0], given: 0

Intern
Joined: 21 Sep 2013
Posts: 1

Kudos [?]: 1 [1], given: 0

### Show Tags

21 Sep 2013, 23:46
1
KUDOS
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18

Kudos [?]: 1 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41686

Kudos [?]: 124440 [5], given: 12078

### Show Tags

22 Sep 2013, 03:57
5
KUDOS
Expert's post
9
This post was
BOOKMARKED
alexgomez2013 wrote:
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18

The answer is 19, not 18. Notice that we have an inequality sign there.

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
A. 17
B. 18
C. 19
D. 20
E. 21

$$P(blue) = \frac{12}{12+y}<\frac{2}{5}$$ --> $$y>18$$ --> $$y_{min}=19$$.

Hope it's clear.
_________________

Kudos [?]: 124440 [5], given: 12078

Current Student
Joined: 06 Sep 2013
Posts: 1988

Kudos [?]: 707 [0], given: 355

Concentration: Finance
Re: From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

25 Nov 2013, 13:52
From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

A. 17
B. 18
C. 19
D. 20
E. 21

It goes like this.

12 Blue
y yellow

12 + y total

12/x = 2/5

So x = 30, x being the total number of ballos
Then yellow> 30-12 = 18

Therefore, yellow must be at least 19

Cheers!
Kudos Rain
J

Kudos [?]: 707 [0], given: 355

Intern
Joined: 03 Jul 2014
Posts: 17

Kudos [?]: 3 [0], given: 19

Re: From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

22 Nov 2014, 03:39
Can u pls help in explaining the shift in the inequilaties symbol .

I mean 12/12+y < 2/5
so
cross multiplying

12*5 < (12+y)2 , am i missing out on reversing the sign ....

Bunuel wrote:
alexgomez2013 wrote:
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18

The answer is 19, not 18. Notice that we have an inequality sign there.

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
A. 17
B. 18
C. 19
D. 20
E. 21

$$P(blue) = \frac{12}{12+y}<\frac{2}{5}$$ --> $$y>18$$ --> $$y_{min}=19$$.

Hope it's clear.

Kudos [?]: 3 [0], given: 19

Math Expert
Joined: 02 Sep 2009
Posts: 41686

Kudos [?]: 124440 [2], given: 12078

From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

22 Nov 2014, 06:50
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
hanschris5 wrote:
Can u pls help in explaining the shift in the inequilaties symbol .

I mean 12/12+y < 2/5
so
cross multiplying

12*5 < (12+y)2 , am i missing out on reversing the sign ....

Bunuel wrote:
alexgomez2013 wrote:
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18

The answer is 19, not 18. Notice that we have an inequality sign there.

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
A. 17
B. 18
C. 19
D. 20
E. 21

$$P(blue) = \frac{12}{12+y}<\frac{2}{5}$$ --> $$y>18$$ --> $$y_{min}=19$$.

Hope it's clear.

It goes like this:
$$\frac{12}{12+y}<\frac{2}{5}$$

Cross multiply: $$60< 24+2y$$;

Subtract 24 from both sides: $$36<2y$$;

Divide by 2: $$18<y$$, which is the same as $$y>18$$ (y is greater than 18).

Hope it's clear.
_________________

Kudos [?]: 124440 [2], given: 12078

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17588

Kudos [?]: 270 [0], given: 0

Re: From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

26 Dec 2015, 19:07
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 [?]: 270 [0], given: 0

Manager
Joined: 25 Dec 2012
Posts: 134

Kudos [?]: 29 [0], given: 148

From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

10 Jan 2016, 03:53
Other way of doing is substitute the value.

The question says it probability of blue should be less than 2/5 means it should be less than 40%

Also For a constant numerator and if the denominator is increasing the value of the output will be decreasing.

In our scenario, the numerator is constant which is 12

Based on the given the choice the denominator will be 12/29, 12/30, 12/31, 12/32, 12/33

Since numerator is same and denominator doesn't vary we can conclude as 12/29 > 12/30 > 12/31 > 12/32 > 12/33

Lets choose the number which is easy to solve. Hence choosing 12/30 first which is equal to 2/5

Straight away I can go for "C" from the above answer since 12/29 must be greater than 2/5 and 12/31 should hold the least value of yellow balls which will give the probability as less than 2/5

Kudos [?]: 29 [0], given: 148

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17588

Kudos [?]: 270 [0], given: 0

Re: From a bag containing 12 identical blue balls, y identical [#permalink]

### Show Tags

20 Jan 2017, 14:21
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 [?]: 270 [0], given: 0

Re: From a bag containing 12 identical blue balls, y identical   [#permalink] 20 Jan 2017, 14:21
Similar topics Replies Last post
Similar
Topics:
3 In a particular gumball machine, there are 4 identical blue gumballs, 2 09 Aug 2017, 13:24
5 A has to pick a ball from a bag with 3 red & 3 blue balls. 12 10 Apr 2017, 04:05
9 Each of the four identical containers (A,B,C and D) contains ‘b’ balls 7 06 Apr 2016, 18:35
2 A box contains exactly 24 balls, of which 12 are red and 12 are blue. 6 09 Jul 2017, 19:20
22 A bag contains ten marbles of the same size: 3 are identical green mar 15 05 Jun 2017, 15:02
Display posts from previous: Sort by
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}