Probability!!!

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Wed May 23, 2012 10:10 am

A box contains identical balls in three different colors - Black, white and blue. There are 8-x blue balls and 2X+5 black balls. If a ball is picked at random from the box, what is the probability that the ball is either blue or black?
1) X=2
2) There are 3X+39 white balls in the box.

OA is [spoiler](B)[/spoiler]

Please explain!!!

Can we expect such extra-ordinary questions in GMAT

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Source: Beat The GMAT — Data Sufficiency | Wed May 23, 2012 10:10 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Wed May 23, 2012 11:10 am

ronnie1985 wrote:A box contains identical balls in three different colors - Black, white and blue. There are 8-x blue balls and 2X+5 black balls. If a ball is picked at random from the box, what is the probability that the ball is either blue or black?
1) X=2
2) There are 3X+39 white balls in the box.

OA is [spoiler](B)[/spoiler]

P(ball is blue or black) = P(blue) + P(black) = (blue balls)/(Total balls) + (black balls)/(Total balls)

Statement(1):
Let 'W' be the white-coloured balls, then
Total balls = (8 - x) + (2x + 5) + W = 13 + x + W
P(blue) + P(black) = (8 - x)/(13 + x + W) + (2x + 5)/(13 + x + W)
x and W are not known.
INSUFFICIENT

Statement(2):
Total Balls = (8 - x) + (2x + 5) + (3x + 39) = 4x + 52
P(blue) + P(black) = (8 - x)/(4x + 52) + (2x + 5)/(4x + 52) = (x + 13)/(4x + 52) = 1/4
SUFFICIENT

[spoiler](B)[/spoiler] is the answer.

So, was there anything 'extraordinary' about it?

Aneesh Bangia
GMAT Math Coach
[email protected]

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed May 23, 2012 11:32 am

Well only solving this particular question would have actually given us a perfectly good answer in the form of B.

If you do not solve the question and from above if you treat this question as if the total is not given, so C should be the answer choice, then you would get the answer as incorrect.

GMAT has this habit of confusing between options C and E and also between C and any of the given options i.e A or B>

Hence the correct answer is B. Be careful...

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