From a bag containing 12 identical blue balls, y identical

[sharmin.karim]

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

A. 17
B. 18
C. 19
D. 20
E. 21

[rags99]

B : 18

P(blue) = 12 / (12+Y)

P(blue) < 2/5


so when you solve: 12 /12+Y = 2/5
y = 18
[editor: this is the solution to the equation, not the inequality. the first proper solution to the inequality is the first number greater than 18, which is 19.
mind the problem you're solving!]


Any other solution.

[tantrix]

B : 18

P(blue) = 12 / (12+Y)

P(blue) < 2/5


so when you solve: 12 /12+Y = 2/5
y = 18


Any other solution.

Shouldn't the answer be 19?

Since you solve for the inequality 12/(12+Y) < 2/5
you end up with y>18

[RonPurewal]

B : 18

P(blue) = 12 / (12+Y)

P(blue) < 2/5


so when you solve: 12 /12+Y = 2/5
y = 18


Any other solution.

Shouldn't the answer be 19?

Since you solve for the inequality 12/(12+Y) < 2/5
you end up with y>18

correct. don't forget that you're dealing with an inequality!

[RonPurewal]

you can also solve this problem by plugging in the answer choices.

note that 2/5 is 40%.

start with (a), since you're looking for the smallest viable solution.
(a) --> this would be 12/29, which is greater than 40%. no go.
(b) --> this would be 12/30, which is exactly 40%. no go.
(c) --> this would be 12/31, which is less than 40%. correct answer.

[asharma8080]

Thank you for the solution Ron. I tried the backsolving approach on this one worked fine however, how were you able to tell so quickly that 12/29 is > 40%, I want to be able to quickly tell this on the exam. My approach was to multiply 29 x 4 and that gave me 116 so that meant it is > 40%.

Thank you in advance.

[RonPurewal]

Thank you for the solution Ron. I tried the backsolving approach on this one worked fine however, how were you able to tell so quickly that 12/29 is > 40%, I want to be able to quickly tell this on the exam. My approach was to multiply 29 x 4 and that gave me 116 so that meant it is > 40%.

Thank you in advance.

12/30 is 0.4, so 12/29 is more than 0.4.