GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 Apr 2018, 01:37

### 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 box contains red and blue balls only. If there are 8 balls in total

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44654
A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

31 Mar 2015, 05:26
2
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:42) correct 45% (01:18) wrong based on 224 sessions

### HideShow timer Statistics

A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________
Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 353
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

31 Mar 2015, 05:41
1
KUDOS
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

1. R(R-1)/(8*7)=5/14
R=5--->Sufficient

2. R(8-R)/(8*7)=15/56
R^2-8R+15=0
R=5 OR 3--->Insufficient

Director
Joined: 07 Aug 2011
Posts: 567
GMAT 1: 630 Q49 V27
A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

31 Mar 2015, 05:47
2
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14\
let N be the number of red balls.
$$\frac{^NC_2}{^8C_2} = \frac{5}{14}$$
N(N-1) = 20
N=5

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.
let N be the number of red balls.
$$\frac{N}{8} * \frac{8-N}{7} = \frac{15}{56}$$
N=5,3
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Current Student
Joined: 25 Nov 2014
Posts: 102
Concentration: Entrepreneurship, Technology
GMAT 1: 680 Q47 V38
GPA: 4
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

31 Mar 2015, 22:02
1
KUDOS
Suppose there are x red balls, and thus, 8-x blue balls.
1) P(both red w/o rep) = x/8 *(x-1)/7 = 5/14. since quad, we'll get 2 values of x, but the no of balls has to be positive. So we take the +ve one. SUFF
2) P(1st red, 2nd blue w/o rep) = x/8 * (8-x)/7 = 15/56 => x*(8-x) = 15. This gives 2 values of x : 5,3. Thus not SUFF, since red balls can be either 5 or 3.

Ans A.
_________________

Kudos!!

Manager
Joined: 28 Jan 2015
Posts: 128
Concentration: General Management, Entrepreneurship
GMAT 1: 670 Q44 V38
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

31 Mar 2015, 22:59
1
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

I went with A

1) Sufficient

x/8 * x/7 = 5/14 <--- solvable and gives ratio. I don't do the actual math, I just know that it's possible....

2) Insufficient
Since the 15/56 results from p(blue)*p(red) there is no way to determine one of them alone from the information given..
Current Student
Joined: 06 Mar 2014
Posts: 258
Location: India
GMAT Date: 04-30-2015
A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

02 Apr 2015, 16:52
1
KUDOS
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

number of red balls (R), number of Blue balls (B)
1) probability that two balls randomly selected without replacement, are red = $$(R/8) * ({R-1}/7) = 5/14$$
we get R(R-1) = 20
R = 5,-4
R cannot be negative so number of red balls (R) = 5

Sufficient Alone.

2) probability that two balls randomly selected without replacement, the first ball is red and the second ball is blue = $$(R/8) * (B/7) = 15/56$$
we get, R*B = 15
we know that R+B = 8
So only possible values are 3 and 5 but which one is red is unclear.
Insufficient Alone.

Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

03 Apr 2015, 15:02
1
KUDOS
R+B=8; R=?
1. 5/14=getting two R w/o replacement=>R(R-1)/8*7=> as R can be only positive so only one answer; Sufficient
2. 15/56=one R one B=>R(8-R)/8*7=> R has two positive values; Not sufficient

Thanks,
Retired Moderator
Joined: 06 Jul 2014
Posts: 1263
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

03 Apr 2015, 16:00
1
KUDOS
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

For this type of question we should only know the principles of probability and don't need to make any calculations to find the correct answer:

We know that this box contain only red and blue balls (important: this approach will be work only for two types of items).
So if we have information about probability randomly selected balls of ONE color (any quantity) we can find how much balls of each color in box.

1) in this statement we have information about probability of two balls the SAME color - this is sufficient and we don't need any calculations, because this is DS task and we should save time

If we have probability for balls with DIFFERENT colors we can't find how much balls of each color in box
2) in this statement we have information about probability of two balls the same color - this is insufficient and we don't need any calculations, because this is DS task and we should save time

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44654
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

06 Apr 2015, 05:39
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

Count_and_Prod_redblue.png [ 36.72 KiB | Viewed 2050 times ]

_________________
Intern
Joined: 11 Apr 2014
Posts: 19
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

15 Jan 2018, 03:17
Bunuel wrote:
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:
Count_and_Prod_redblue.png

Hi All,
WRT official soln

is it not (RB / 56 ) = 1/2 * ( 15/56) because there are two ways ...

1. Non red & then red
2. Red and then non red.

Kindly clarify
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1033
Location: India
Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]

### Show Tags

19 Jan 2018, 07:29
coolnaren wrote:
Bunuel wrote:
Bunuel wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:
Count_and_Prod_redblue.png

Hi All,
WRT official soln

is it not (RB / 56 ) = 1/2 * ( 15/56) because there are two ways ...

1. Non red & then red
2. Red and then non red.

Kindly clarify

Hi

Second statement clearly specifies that the probability of selecting first ball as red and second ball as blue is = 15/56. So its only the second case:- out of the two cases specified by you.
Re: A box contains red and blue balls only. If there are 8 balls in total   [#permalink] 19 Jan 2018, 07:29
Display posts from previous: Sort by