Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46991

A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
31 Mar 2015, 05:26
Question Stats:
56% (01:41) correct 44% (01:18) wrong based on 232 sessions
HideShow timer Statistics



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: 349

Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
31 Mar 2015, 05:41
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(R1)/(8*7)=5/14 R=5>Sufficient 2. R(8R)/(8*7)=15/56 R^28R+15=0 R=5 OR 3>Insufficient Answer: A



Director
Joined: 07 Aug 2011
Posts: 561
Concentration: International Business, Technology

A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
31 Mar 2015, 05:47
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. Answer A . (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(N1) = 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. \(\frac{N}{8} * \frac{8N}{7} = \frac{15}{56}\) N=5,3
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Current Student
Joined: 25 Nov 2014
Posts: 102
Concentration: Entrepreneurship, Technology
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
Suppose there are x red balls, and thus, 8x blue balls. 1) P(both red w/o rep) = x/8 *(x1)/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 * (8x)/7 = 15/56 => x*(8x) = 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: 129
Concentration: General Management, Entrepreneurship

Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
31 Mar 2015, 22:59
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: 257
Location: India
GMAT Date: 04302015

A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
02 Apr 2015, 16:52
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 = \((R/8) * ({R1}/7) = 5/14\) we get R(R1) = 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. Answer:A



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
R+B=8; R=? 1. 5/14=getting two R w/o replacement=>R(R1)/8*7=> as R can be only positive so only one answer; Sufficient 2. 15/56=one R one B=>R(8R)/8*7=> R has two positive values; Not sufficient Hence answer is A
Thanks,



Retired Moderator
Joined: 06 Jul 2014
Posts: 1248
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
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 So answer is A
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Math Expert
Joined: 02 Sep 2009
Posts: 46991

Re: A box contains red and blue balls only. If there are 8 balls in total [#permalink]
Show Tags
06 Apr 2015, 05:39



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: 1270
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






