Hi..

The question is correct as it is...
1) statement tells probability is 1/10
So if total is <=30, total number could be 10,20 or 30
If total is <30, total can be 10 or 20
2) statement II tells us that blue is 10
if total is 30, red is 3 and if total is 20 red is 2.
Insufficient

Combined...
If total can be 10,20,30 and blue is 10, total will be >10 as there is at least one red..
But if total <30 and >10, total can be only 20, so red is 2..
Blue -10, red-2 and other colours/colour-8 ( we are not concerned what other colours are, we are only concerned with red)
So sufficient
C
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Just a small correction in the last bit:

Combining 1 & 2 we know total number of blue balls is 10, so total number of red balls has to be less than 20 (because total balls is less than 30). Hence number of red balls is 1.

Total balls \(<30\)

Statement 1: implies ratio of number of red balls to total number of balls \(= 1:10\). so let total red balls be \(x\) and total number of balls be \(10x\)

given \(10x<30=> x<3\)

So red balls can be \(1\) or \(2\) and total number of balls can be \(10\) or \(20\). So No unique answer. Insufficient

Statement 2: Nothing mentioned about red balls. Insufficient

Combining 1 & 2 we know total number of blue balls is \(10\), so total number of balls has to be \(20\). Hence number of red balls is \(2\). Sufficient

Option C

Good Morning

I do not agree. Nowhere it is mentioned that the bag has only red and blue balls

Hi arichinna

Thanks for highlighting but I feel the the question needs to be changed to less than or equal to 30, other wise statement 1 will not hold

Hi atreyu79

You do not need to know how many types of balls are there. You simply need to know total number of balls and relationship between total number of balls and number of red balls. this information can be arrived at by combining both the statements.
However I also feel a slight correction needs to be made in the question stem. the bag must have less than OR EQUAL to 30 balls.