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

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Math Expert
Joined: 02 Aug 2009
Posts: 6792
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 05:34
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55% (hard)

Question Stats:

45% (01:20) correct 55% (00:57) wrong based on 65 sessions

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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 .

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 21 Jun 2014
Posts: 64
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 05:55
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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Manager
Joined: 23 Jun 2016
Posts: 118
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 06:51
saicharan1191 wrote:
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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E
Why can’t
r = b = w = 3?

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Manager
Joined: 14 Sep 2016
Posts: 145
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 06:53
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.

Manager
Joined: 14 Sep 2016
Posts: 145
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 06:54
sevenplusplus wrote:
saicharan1191 wrote:
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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

E
Why can’t
r = b = w = 3?

Sent from my iPhone using GMAT Club Forum mobile app

Question has mentioned that no. of red, blue and white balls are different. hence, we can't consider it as equal.
Manager
Joined: 23 Jun 2016
Posts: 118
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 06:56
kunalsinghNS wrote:
sevenplusplus wrote:
saicharan1191 wrote:
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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

E
Why can’t
r = b = w = 3?

Sent from my iPhone using GMAT Club Forum mobile app

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

Missed that. Thanks.

Sent from my iPhone using GMAT Club Forum mobile app
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Posts: 1212
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If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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Updated on: 28 Oct 2017, 08:14
1
chetan2u wrote:
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 .

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

Originally posted by niks18 on 28 Oct 2017, 07:30.
Last edited by niks18 on 28 Oct 2017, 08:14, edited 1 time in total.
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Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 07:36
kunalsinghNS wrote:
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.

Hi kunalsinghNS,

Can you explain your reason for rejecting statement 1?
Math Expert
Joined: 02 Aug 2009
Posts: 6792
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 07:41
niks18 wrote:
kunalsinghNS wrote:
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.

Hi kunalsinghNS,

Can you explain your reason for rejecting statement 1?

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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1212
Location: India
GPA: 3.82
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 07:50
chetan2u wrote:
niks18 wrote:
kunalsinghNS wrote:
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.

Hi kunalsinghNS,

Can you explain your reason for rejecting statement 1?

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

I completely missed that
can you explain what is missing in my assumption?
Math Expert
Joined: 02 Aug 2009
Posts: 6792
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 08:03
niks18 wrote:
chetan2u wrote:
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 .

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 $$r$$ to be prime $$\frac{b^2}{w}$$ has to be prime. let $$\frac{b^2}{w}=p$$, where $$p$$ is any prime no

so $$b^2=p*w => b=\sqrt{p*w}$$

so for $$b$$ to be an integer $$p=w$$ which in turn will mean that $$b=w=p$$ which is not possible. Hence $$r$$ is not prime. Sufficient

Statement 2: nothing mentioned about $$r$$. Insufficient

Option A

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 $$p*w= 2*3^2*2=36$$
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1212
Location: India
GPA: 3.82
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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28 Oct 2017, 08:06
chetan2u wrote:
niks18 wrote:
chetan2u wrote:
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 .

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 $$r$$ to be prime $$\frac{b^2}{w}$$ has to be prime. let $$\frac{b^2}{w}=p$$, where $$p$$ is any prime no

so $$b^2=p*w => b=\sqrt{p*w}$$

so for $$b$$ to be an integer $$p=w$$ which in turn will mean that $$b=w=p$$ which is not possible. Hence $$r$$ is not prime. Sufficient

Statement 2: nothing mentioned about $$r$$. Insufficient

Option A

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 $$p*w= 2*3^2*2=36$$

Yes agreed completely missed the point
Senior Manager
Joined: 02 Apr 2014
Posts: 477
GMAT 1: 700 Q50 V34
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

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21 Dec 2017, 12:49
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
If there are different numbers of red, blue and white balls, is the nu &nbs [#permalink] 21 Dec 2017, 12:49
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