If there is a bag containing less than 30 balls, how many of them are

Question

If there is a bag containing less than 30 balls, how many of them are red balls?

(1) The probability of picking a red ball from the bag is  \frac{1}{10} .
(2) There are 10 blue ball in the bag.

source : self made

atreyu79 · Accepted Answer

Good Morning

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

chetan2u · Answer

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

niks18 · Answer

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

arichinna · Answer

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.

niks18 · Answer

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

niks18 · Answer

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.

vanquisher · Answer

I think in this question we have to assume that there can only be two types of ball i.e red and blue coloured ball , then only the option C is correct. If we assume multiple coloured balls then I think the answer will be E.

@Bunuel

@ Bunuel

chetan2u · Answer

It does not matter whether there are multiple colours or just red and blue..
 Statement 1 tells us that the number of balls are multiple of 10 and there is atleast one red ball. As the number of balls are <30, there are either 10 total balls with just one red in them or there are 20 red balls with 2 red balls.
But statement 2 tells us that there are 10 blue balls, so total balls have to be more than 10.
Combining above two, only possibility is of having 20 balls in which 2 are red

zitipiti · Answer

statement 1 alone: Red balls could be 1 (out of 10) or 2 (out of 20). Insufficient. 
statement 2 alone: Knowing there are 10 blue balls tells us nothing about red balls. Insufficient.
Combined: If the total were 10, you couldn't have 10 blue balls   and    any red balls. Thus, the total must be 20, meaning there are exactly 2 red balls.

Tinytrotter · Answer

We know that the total number of balls in the bag are < 30.

Statement 1 tells us probability of picking a red ball is 1/10. Now note that for the denominator to be a perfect 10 and we can't have decimals when whole balls are concerned, the total number of balls can be 10 or 20 (Not 30 because total number of balls is lesser than 30)

But we still do not know whether red balls are 1 (in case of total 10 balls) or 2 (in case of total 20 balls). INSUFFICIENT

Statement 2 tells us there are total 10 balls. Standalone this statement is not useful because we do not get any idea on how many red balls there are.

Now combining Statement 1 and 2.

As per Statement 1 - we had 2 cases for the total number of balls i.e. either 10 or 20.

Statement 2 tells us that there are 10 Blue Balls. Plus, we also know that there is 1/10 chance of picking red balls which means there is at least 1 red ball in the bag.

This tells us that total number of balls cannot be 10 (because minimum is 10 blue balls + 1 red ball i.e 11)

This means we are now in case 2 where total number of balls is 20 (of which 10 are blue, 2 are red - as 1/10 is probability of getting red, and 8 are other unknown colors) But now we know definitively that there are only 2 red balls in the bag.

Hence (C) is sufficient.

LessGoRahul · Answer

chetan2u 
this is not a valid question as there is still a probability of having boll of any other color , it is not specified that there are only 2type of balls

chetan2u · Answer

Rahul
What do you think the answer will be if 
1. There are two colors incl Red.
2. There are three colours incl Red.

Other colours do not matter here. That is what the question is all about.

Mehta17 · Answer

Since probability is 1/10, and total balls are less than 30 
Red balls can be either 10 or 20

Option A - Not sufficient

But if we take option B also then, 10 blue balls which means total balls has to be 20 
Hence
A+ B = sufficient - Option C

If there is a bag containing less than 30 balls, how many of them are

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If there is a bag containing less than 30 balls, how many of them are

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