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

 It is currently 27 Jun 2019, 03:28

### 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

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

# a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 22 Aug 2013
Posts: 1437
Location: India
a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

08 Jan 2019, 22:32
4
00:00

Difficulty:

95% (hard)

Question Stats:

24% (02:36) correct 76% (02:28) wrong based on 50 sessions

### HideShow timer Statistics

a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N, such that (a+b+c) is not equal to 0.
Also M is a positive number. Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.
CEO
Joined: 18 Aug 2017
Posts: 3947
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

09 Jan 2019, 06:19
1
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive integer.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.

amanvermagmat

is the question posted correct?
in the question stem it says M is a +ve integer , but in #1 M is given as a fraction..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Retired Moderator
Joined: 22 Aug 2013
Posts: 1437
Location: India
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

09 Jan 2019, 22:53
Archit3110 wrote:
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive integer.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.

amanvermagmat

is the question posted correct?
in the question stem it says M is a +ve integer , but in #1 M is given as a fraction..

Thanks for pointing that out. Editing the question right now.
Manager
Joined: 18 Apr 2018
Posts: 93
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

10 Jan 2019, 00:42
amanvermagmat I still don't understand how statement 2 is not sufficient. M is definitely a positive non integer, since k is an odd integer and N = -1.

Posted from my mobile device
SVP
Joined: 26 Mar 2013
Posts: 2254
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

10 Jan 2019, 01:14
1
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive number.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.

Hi amanvermagmat

Are you sure from the OA.

(1) M = 3/2

Let a=b=c=1...N= 1/2

M+N = 1/2 + 3/2= 4/2 = 2.........(M+N)/2 = 1..........Answer is Yes

Let a=1 b= 2 c=-3...N= -1

M+N = -1+ 3/2 = 1/2.........(M+N)/2 = 1/4................Answer is No

Insufficient
Retired Moderator
Joined: 22 Aug 2013
Posts: 1437
Location: India
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

10 Jan 2019, 03:09
2
1
Mo2men wrote:
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive number.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.

Hi amanvermagmat

Are you sure from the OA.

(1) M = 3/2

Let a=b=c=1...N= 1/2

M+N = 1/2 + 3/2= 4/2 = 2.........(M+N)/2 = 1..........Answer is Yes

Let a=1 b= 2 c=-3...N= -1

M+N = -1+ 3/2 = 1/2.........(M+N)/2 = 1/4................Answer is No

Insufficient

Hello

Thanks for your query. I have again edited the question in light of this new information.

Well -if three or more ratios are equal, say p/q = r/s = t/u = .... (and so on)
then each of these ratios is also equal to = (p+r+t+...)/(q+s+u+...) , i.e., each of these ratios is equal to the ratio of sum of numerators and the sum of denominators.

So in my question: a/(b+c) = b/(c+a) = c/(a+b) = N.. Here N is also = (a+b+c)/(b+c+c+a+a+b) = (a+b+c)/2(a+b+c) .
Since a+b+c is coming in denominator, we CANNOT take those values where a+b+c = 0.
In your second example: a=1 b= 2 c=-3... a+b+c = 0 which is not allowed.

This should have been mentioned in the question, so I am editing now. Thanks for this query.
SVP
Joined: 26 Mar 2013
Posts: 2254
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

### Show Tags

10 Jan 2019, 03:22
amanvermagmat wrote:
Hello

Thanks for your query. I have again edited the question in light of this new information.

Well -if three or more ratios are equal, say p/q = r/s = t/u = .... (and so on)
then each of these ratios is also equal to = (p+r+t+...)/(q+s+u+...) , i.e., each of these ratios is equal to the ratio of sum of numerators and the sum of denominators.

So in my question: a/(b+c) = b/(c+a) = c/(a+b) = N.. Here N is also = (a+b+c)/(b+c+c+a+a+b) = (a+b+c)/2(a+b+c) .
Since a+b+c is coming in denominator, we CANNOT take those values where a+b+c = 0.
In your second example: a=1 b= 2 c=-3... a+b+c = 0 which is not allowed.

This should have been mentioned in the question, so I am editing now. Thanks for this query.

Hi amanvermagmat

Thanks for your reply and the nice rule that I learnt from you today.
Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N   [#permalink] 10 Jan 2019, 03:22
Display posts from previous: Sort by