If there are different numbers of red, blue and white balls, is the nu

Question

If there are different numbers of red, blue and white balls, is the number of red ball equal to a prime number?

(1) The ratio of red to blue ball is same as ratio of blue to white.
(2) The number of blue ball is equal to a prime number .

source-self made

saicharan1191 · Answer

Is it C?
St 1: b^2 =rw 
r can be prime or composite
ex: b= 10, r can be 20 or 5
St 2: R can be anything again.

1+2 
B is prime , b^2= rw 
It means either b=r=w or r= 1, w= b^2 or r= b^2, w= 1
Given the numbers are different, so r= 1 or b^2
In either case it is not prime.

So C

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sevenplusplus · Answer

E
Why can’t
r = b = w = 3?

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kunalsinghNS · Answer

Statement 1 & 2 are alone insufficient

taking both option together we get :

r = b^2/w and we know that r is an integer. hence, since b is not equal to w and b^2/w is an integer. we, can conclude that r = 1, which is not a prime number.

Answer = C

kunalsinghNS · Answer

Question has mentioned that no. of red, blue and white balls are different. hence, we can't consider it as equal.

sevenplusplus · Answer

Missed that. Thanks.

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niks18 · Answer

Statement 1 : given  \frac{r}{b}=\frac{b}{w} => r=\frac{b^2}{w}

Case 1: if,  w=1 , then  r=b^2  i.e a perfect square hence cannot be prime

Case 2: if,  w≠1 , then for  r  is prime if  \frac{b^2}{w}  is prime and if  \frac{b^2}{w}  is a composite no, then  r  is not prime.  Insufficient

Statement 2 : nothing mentioned about  r .  Insufficient

Combining 1 & 2, given  b  is prime so for  r=\frac{b^2}{w}  to be an integer  w=1 , hence  r  is not prime.  Sufficient

Option  C

niks18 · Answer

Hi  kunalsinghNS ,

Can you explain your reason for rejecting statement 1?

chetan2u · Answer

Hi...
r:B:w is 20:10:5.....ans NO ratio is 2:1
r:b:w is 5:10:20......ans YES ratio is 1:2

niks18 · Answer

I completely missed that

can you explain what is missing in my assumption?

chetan2u · Answer

hi,

you have gone wrong in the coloured portion..
 b^2=P_1*w => b=\sqrt{P_1*w}

here w can be easily  P_2^2*P_1 
say p*w, p is any prime number say 2, w could be  3^2*2  so  p*w= 2*3^2*2=36

niks18 · Answer

Yes agreed completely missed the point

hellosanthosh2k2 · Answer

Statement 1:  R/B = B/W 
  B^2 = RW 
 => tempting to say it as sufficient to say R is not prime number
 => But not so.., R can be 2, W = can be odd power of 2, say W = 8 => B = 4 => R is prime
 => insufficient

Statement 2: clearly insufficient

(1) + (2) =>  B^2 = R * W  =>  Prime^2 = R * W 
 since R cannot be same as W,
 either  R = prime^2  and  W = 1 
 or R = 1,  W = prime^2  => either ways, R is not prime number, => (C)

Excellent question  chetan2u

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If there are different numbers of red, blue and white balls, is the nu

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