GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 22:14 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If there are different numbers of red, blue and white balls, is the nu

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 7686
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

1
4 00:00

Difficulty:   85% (hard)

Question Stats: 44% (02:25) correct 56% (02:09) wrong based on 62 sessions

### HideShow timer Statistics

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

_________________
Manager  B
Joined: 21 Jun 2014
Posts: 62
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

1
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
Manager  B
Joined: 23 Jun 2016
Posts: 94
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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
Manager  B
Joined: 14 Sep 2016
Posts: 129
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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
Manager  B
Joined: 14 Sep 2016
Posts: 129
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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  B
Joined: 23 Jun 2016
Posts: 94
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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 .

source-self made

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.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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.

Answer = C

Hi kunalsinghNS,

Can you explain your reason for rejecting statement 1?
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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.

Answer = C

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
_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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.

Answer = C

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 V
Joined: 02 Aug 2009
Posts: 7686
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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 .

source-self made

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 $$p*w= 2*3^2*2=36$$
_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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 .

source-self made

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  G
Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

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
Non-Human User Joined: 09 Sep 2013
Posts: 11012
Re: If there are different numbers of red, blue and white balls, is the nu  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If there are different numbers of red, blue and white balls, is the nu   [#permalink] 06 Feb 2019, 09:53
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  