Problem Solving

From a bag containing 12 blue balls, y yellow ball, and no ther balls, one ball will be removed at random. If the probability of selecting a blue ball is less than 2/5, what is the least number of yellow balls that must be in the bag?
1-17
2-18
3-19
4-20
5-21

I keep getting 18, OA is 19. Can someone please explain and/or tell me where I am going wrong? Thanks guys

maolivie wrote:From a bag containing 12 blue balls, y yellow ball, and no ther balls, one ball will be removed at random. If the probability of selecting a blue ball is less than 2/5, what is the least number of yellow balls that must be in the bag?
1-17
2-18
3-19
4-20
5-21

I keep getting 18, OA is 19. Can someone please explain and/or tell me where I am going wrong? Thanks guys

Let's assume that the probability is EXACTLY 2/5 that you'll pull out a blue ball. So, if you have 12 blue balls,

12/x = 2/5
2x = 60
x = 30 => which means you need 30 balls total.

So,
(total balls - blue balls = yellow balls)
30 - 12 = 18

So you have 18 yellow balls. Looks like you got up to here all okay.

However, this means that you need 18 balls if you need the probability of pulling out a blue ball to be exactly 2/5. To make the probability less than 2/5, you would need to add 1 more yellow ball, so answer = 19.

thanks again termis. This must be why my weakpoint for the GMAT in the verbal section is CR - I don't read carefully enough. How can I fix this?

maolivie wrote:thanks again termis. This must be why my weakpoint for the GMAT in the verbal section is CR - I don't read carefully enough. How can I fix this?

I'm no better, really. I've been doing sets of problems on a regular basis for 4 months now, so I do catch myself more often before I do something silly, but I still do it once in awhile. When I see the solution, it kills me that I overlooked something so simple, but hey, you and I are definitely not alone.

After you select an answer, just read the question quickly and see if it makes sense. But above all, just keep on hammering away at different questions on a regular basis, and you should get the hang of it over time.

Here's How I did it :

Let yellow balls in the bag be Y

so,its given that

12/12+Y < 2/5

12 is the no. of blue balls, 12+Y is total no. of possible outcomes i.e. total no. of balls (blue+yellow)
Simplifying, solving the inequality

2Y + 24 > 60
Y + 12 > 30

Y > 18,

So,minimum value Y can take is 19