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655-705 Level|   Probability|      
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siddharthkapoor
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A box has 10 balls, either red or blue. If two balls are to be drawn s 05 Sep 2020, 22:24
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A
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65% (hard)

Question Stats:

57% (02:10) correct 43% (02:14) wrong based on 242 sessions

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A box has 10 balls, either red or blue. If two balls are to be drawn simultaneously from the box, what is the number of red balls?

(1) The probability that the two balls drawn will be red is 1/15.
(2) The probability that one of the balls drawn will be red and the other will be blue is 7/15.
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A
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A box has 10 balls, either red or blue. If two balls are to be drawn s 06 Sep 2020, 09:03
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This is almost an exact copy of an official question, with the "less than half" restriction removed (which makes S2 insufficient in this version). The original version is here, with complete solutions:

https://gmatclub.com/forum/a-box-contai ... 99940.html

The writing in the official question is much better than in this one (the question here technically doesn't make any sense - the number of red balls does not depend on the fact that we're selecting two of them, but that's what the wording here implies), so the official version is the one worth studying.
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A box has 10 balls, either red or blue. If two balls are to be drawn s 06 Sep 2020, 11:25
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siddharthkapoor
A box has 10 balls, either red or blue. If two balls are to be drawn simultaneously from the box, what is the number of red balls?

(1) The probability that the two balls drawn will be red is 1/15.
(2) The probability that one of the balls drawn will be red and the other will be blue is 7/15.

1> -- R(R-1) = 6 => R = 3 -- Sufficient

2> R B / 90 = 7/15 = > not Sufficient

So A is the ans
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A box has 10 balls, either red or blue. If two balls are to be drawn s 05 Nov 2020, 23:09
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Let r - no. of red balls and b- no. of blue balls
r+b = 10 (given)
Statement 1: Prob(two reds) = 1/15
Hence, rC2 / 10C2 = 1/15
=> r(r-1) = 6
=> r=3
sufficent

Statment 2 : Prob (one of each r and b) = 7/15
Hence, (rC1*bC1)/ 10C2 = 7/15
=> r*b = 21
and r+b = 10 (given)
=> r,b =3,7
But, it doesn't tell us if r is 3 or 7
Hence, not sufficient

Correct answer - A
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A box has 10 balls, either red or blue. If two balls are to be drawn s 12 Feb 2021, 21:03
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This is how I thought about it.

R = ?

St1- P(two red) = 1/15

(r/10) x (r-1/ 9) = 1/15 <--- r is the number of reds
Sufficient.

St2 - P(blue and red) = 7/15

i) blue,red : b/10 x r/9
ii) red,blue: r/10 x b/9

(b/10 x r/9) + (r/10 x b/9) = rb / 45

Insufficient

Answer is A.
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A box has 10 balls, either red or blue. If two balls are to be drawn s 28 Dec 2023, 07:19
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