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

 It is currently 24 Apr 2019, 13:28

### 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

# Last Monday N female executives (N>1) received M male managers (M>1)

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 932
Last Monday N female executives (N>1) received M male managers (M>1)  [#permalink]

### Show Tags

26 Mar 2019, 07:32
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:04) correct 50% (02:15) wrong based on 24 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 18)

Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?

(1) M < 11
(2) M(M+2N) = 65

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 19 Jan 2019
Posts: 72
Re: Last Monday N female executives (N>1) received M male managers (M>1)  [#permalink]

### Show Tags

26 Mar 2019, 08:10
The question is simply asking what are the values of m and n... (Both are integers)..

Statement 1 is clearly not sufficient as m and n can take numerous values...

Statement 2 -
M(m + 2n) = 65
Now factors of 65 include 1,5,13,65...

(1,65) are ruled out since both m and n are greater than 1..

M(m+2n) = 5*13
M = 5 , 5+2n = 13
N = 4... Bingo... That's all what we need.... (We cannot take m as 13 because taking m as 13 would give n a negative value).

Statement 2 individually is sufficient to answer the question..

Posted from my mobile device
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 932
Last Monday N female executives (N>1) received M male managers (M>1)  [#permalink]

### Show Tags

26 Mar 2019, 14:39
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?

(1) M < 11
(2) M(M+2N) = 65

$$m,n\,\, \ge \,\,2\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$

$$? = C\left( {m + n,2} \right) - C\left( {n,2} \right) = {{\left( {m + n} \right)\left( {m + n - 1} \right)} \over 2} - {{n\left( {n - 1} \right)} \over 2}$$

$$? = \frac{{m\left( {m + n - 1} \right) + nm + n\left( {n - 1} \right) - n\left( {n - 1} \right)}}{2} = \,\,\frac{{m\left( {m + 2n - 1} \right)}}{2}\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,? = \frac{{m\left( {m + 2n - 1} \right)}}{2}\,}$$

$$\left( 1 \right)\,\,m < 11\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{5}} \hfill \cr \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,3} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\, \ne \,\,{\rm{5}}\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,m\left( {m + 2n} \right) = 65 = 5 \cdot 13\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)\,\,{\rm{and}}\,\,\left( {**} \right)} \,\,\,\,\left( {m,m + 2n} \right) = \left( {5,13} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( {**} \right)\,\,\,m > m + 2n\,\,\,\,\, \Rightarrow \,\,\,n < 0\,\,\,\,\,\,{\rm{impossible}}$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Last Monday N female executives (N>1) received M male managers (M>1)   [#permalink] 26 Mar 2019, 14:39
Display posts from previous: Sort by