12 Days of Christmas GMAT Competition - Day 7: A jar contains only

A jar contains only green and red candies. If the ratio of green candies to red candies in the jar is 8 to 3, what is the number of red candies in the jar?

(1) The minimum number of candies one must pick from the jar to ensure getting at least one candy of each color is 25.
(2) The probability of randomly picking a red candy from the jar is 3/11.



Bunuel What is wrong with my solution? From statement one we can get minimum 24 candies of either color. Thus, red could be either 9 or 24.

\(\frac{Green}{Red} = \frac{8}{3}\)

Red candies = ?

(1) The minimum number of candies one must pick from the jar to ensure getting at least one candy of each color is 25.

One of them must be 24 in number. It could be either green or red.

If Green = 24 then Red = 9
If Red = 24 then Green = 64

Multiple answers. Insufficient.

(2) The probability of randomly picking a red candy from the jar is 3/11.

This does not provide any new information. Insufficient.

(3) Combining both statements

If Green = 24 then Red = 9.
Probability of Red = \(\frac{9}{33} = \frac{3}{11}\)

If Red = 24 then Green = 64
Probability of Red = \(\frac{24}{88} = \frac{3}{11}\)

Insufficient. E IMO

Green Candies = 8x
Red Candies = 3x

(1) The minimum number of candies one must pick from the jar to ensure getting at least one candy of each color is 25.

As red candies are fewer in number, we need to pick up 3x + 1 candies to ensure getting at least one candy of each color.

3x + 1 = 25

3x = 24

Sufficient.

(2) The probability of randomly picking a red candy from the jar is 3/11.

3x/11x = 3/11

This statement is not sufficient as x cancels out.

IMO A