It is currently 23 Oct 2017, 10:40

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a class comprising boys and girls, there were 45 hand

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Director
Joined: 26 Sep 2005
Posts: 570

Kudos [?]: 24 [0], given: 0

Location: Munich,Germany
In a class comprising boys and girls, there were 45 hand [#permalink]

Show Tags

02 Mar 2006, 04:17
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?

25
15
150
300
24

Kudos [?]: 24 [0], given: 0

Manager
Joined: 14 Jun 2005
Posts: 99

Kudos [?]: 19 [0], given: 0

Show Tags

02 Mar 2006, 08:50
I got 150.

I did trial and error to get 45 handshakes among X girls. 45=XC2. After a couple of tries, I got X=10.

For Y boys, 105=YC2. So, Y=15.

Between boys and girls is X*Y=10*15=150.

Kudos [?]: 19 [0], given: 0

Manager
Joined: 24 Dec 2005
Posts: 94

Kudos [?]: 9 [0], given: 0

Show Tags

02 Mar 2006, 09:51
Logically speaking this is what I get.

No of Girls = n(n+1)/2 = 45, hence n = 9
No of Boys = n(n+1)/2 = 105. hence n = 14

Handshakes between a boy and a girl = 14*9 = 126.

Kudos [?]: 9 [0], given: 0

Manager
Joined: 01 Feb 2006
Posts: 98

Kudos [?]: [0], given: 0

Show Tags

02 Mar 2006, 10:05
g = # of girls; b=#of boys
gC2 = 45
therefore...
g!/2!(g-2)! = 45
g(g-1)!/2! = 45
g(g-1) = 45 x 2
g^2 - g = 90.......resolves to 10

after following same steps..
b^2 - b = 210......resolves to 15

handshakes btw boys and girls = 15 x 10 = 150

Kudos [?]: [0], given: 0

Manager
Joined: 01 Feb 2006
Posts: 98

Kudos [?]: [0], given: 0

Show Tags

02 Mar 2006, 10:12
Gordon wrote:
Logically speaking this is what I get.

No of Girls = n(n+1)/2 = 45, hence n = 9
No of Boys = n(n+1)/2 = 105. hence n = 14

Handshakes between a boy and a girl = 14*9 = 126.

You method is a much quicker way to solve the problem but your mistake is:
# of Girls should be n(n-1)/2 = 45 and # of boys should be n(n-1)/2 = 105

Last edited by trublu on 02 Mar 2006, 11:21, edited 1 time in total.

Kudos [?]: [0], given: 0

Manager
Joined: 24 Dec 2005
Posts: 94

Kudos [?]: 9 [0], given: 0

Show Tags

02 Mar 2006, 10:32
trublu my friend, u got me out of potential trouble:). Thanks for pointing that out.

Kudos [?]: 9 [0], given: 0

Manager
Joined: 24 Oct 2005
Posts: 169

Kudos [?]: 206 [0], given: 0

Show Tags

03 Mar 2006, 13:58
Hey Guys...this is really one of my weaknesses. Could you explain the logic for setting up the equation n(n-1)/2....

Kudos [?]: 206 [0], given: 0

Intern
Joined: 28 Feb 2006
Posts: 4

Kudos [?]: [0], given: 0

C if this helps [#permalink]

Show Tags

04 Mar 2006, 01:31
If there are 10 girls, the handshakes go as :
1st girl = 9
2nd girl = 8
.....
10th girl = 0
So, it is 9+8+.....+1+0 = Sum of natural numbers upto 9 = 9*10/2 = 45

Now, if we use the formula of sum of natural numbers taking N=10,
then, N (N+1)/2 , for 10 girls becomes 10 * 11 / 2 = 55.

Whereas, the question asked is about handshakes between the girls and not the girls,
we need to consider 9 + 8 +....... + 1
which boils down to N (=9 ) * N+1 (=10) / 2

But, if we want a direct answer, we can take N as 10 girls, in which case
formula has to be considered as N(N-1)/2.
_________________

Kudos [?]: [0], given: 0

Manager
Joined: 20 Mar 2005
Posts: 201

Kudos [?]: 16 [0], given: 0

Location: Colombia, South America

Show Tags

04 Mar 2006, 11:19
positive soul wrote:
Hey Guys...this is really one of my weaknesses. Could you explain the logic for setting up the equation n(n-1)/2....

that is pretty simple just think about adding the numbers from 1 to 100

then you can add 1+100 = 101
2+99 = 101
3+98 = 101
.....
50+51 =101

so you have 50 pairs that add 101

so for the number 100

n=100

then n(n+1)/2 = 50*(101)

some people say that Gauss found out this when he was 5 years old

Kudos [?]: 16 [0], given: 0

SVP
Joined: 14 Dec 2004
Posts: 1681

Kudos [?]: 169 [0], given: 0

Show Tags

05 Mar 2006, 05:33
positive soul wrote:
Hey Guys...this is really one of my weaknesses. Could you explain the logic for setting up the equation n(n-1)/2....

We can get this equation by normal combination ...

Handshakes among girls = 45
Let number of girls be = n
=> so, total handshakes are nC2 = n!/[(n-2)! * 2!] = n*(n-1)/2

i.e. n*(n-1)/2 = 45. then solve for n & we get n = 10

Similarly for boys, m*(m-1) = 105. then solve for m & we get m = 15

So answer is, 15*10 = 150

Kudos [?]: 169 [0], given: 0

05 Mar 2006, 05:33
Display posts from previous: Sort by

In a class comprising boys and girls, there were 45 hand

 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®.