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15 Oct 2024, 01:30
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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.
(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.
This is a Data Sufficiency Butler Question
Check the links to other Butler Projects:
Check the links to other Butler Projects:
- Data Sufficiency Butler
- Problem Solving Butler
- Sentence Correction Butler
- Reading Comprehension Butler
- Integrated Reasoning Butler
15 Oct 2024, 10:44
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R+B=8
we are looking for R.
statement 1 : R(R-1)/56 = 5/14 which means 14R^2 -14R-280=0
Solve for R, R=5 sufficient
statement 2 alone:
RB/56=15/56 ie RB=15
since R+B=8, R^2+15=8R ie R=3 or R=5 insufficient
Answer A.
we are looking for R.
statement 1 : R(R-1)/56 = 5/14 which means 14R^2 -14R-280=0
Solve for R, R=5 sufficient
statement 2 alone:
RB/56=15/56 ie RB=15
since R+B=8, R^2+15=8R ie R=3 or R=5 insufficient
Answer A.
15 Oct 2024, 19:29
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given = r+b= 8 Find = # of r.
Statement 1: rC2/8C2 =5/14
r(r-1)/8*7 = 5/14
r(r−1)=20
r^2-r-20=0
(r−5)(r+4)=0
r= 4
SUFFICIENT.
Statement:2
rC1*8-rC1/8C2/8C2= 15/56
r*(8-r)/56 = 15/56
r^2-8r+15=0
r= 5,3 INSUFFICIENT.
Statement 1: rC2/8C2 =5/14
r(r-1)/8*7 = 5/14
r(r−1)=20
r^2-r-20=0
(r−5)(r+4)=0
r= 4
SUFFICIENT.
Statement:2
rC1*8-rC1/8C2/8C2= 15/56
r*(8-r)/56 = 15/56
r^2-8r+15=0
r= 5,3 INSUFFICIENT.
