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

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Bunuel
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In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   20 Jan 2022, 08:49
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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?

A. 15
B. 24
C. 25
D. 150
E. 300
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JerryAtDreamScore
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In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   20 Jan 2022, 08:58
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Bunuel wrote:
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?

A. 15
B. 24
C. 25
D. 150
E. 300


Breaking Down the Info:

First, we need to find the number of handshakes made with n people.

Each person should handshake each other person (n - 1 people). Repeat this for all n people so that would be \(n*(n - 1)\) handshakes in total. The flaw with this method is that it double counts A shaking with B then B shaking with A, so we must divide that by 2 to get the real number of handshakes, which is \(\frac{n*(n - 1)}{2}\).

Now we may set \(\frac{n*(n - 1)}{2} = 45 \text{ or } 105\) to find \(n = 10\) or \(n = 15\) (10*9= 90 and 15*14 = 210).

Thus there are 25 students in the class, and plugging this in the formula gives \(25*12 = 300\).

Answer: E
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Re: In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   13 Jul 2022, 09:21
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Ans is 150

No of girls - g
No of handshake - g(g-1)/2=45
G =10

No of boys - b
No of handshake - b(b-1)/2 = 105
B =15

Total PPL = 10+15=25
Total handshake= 25*24/2= 300
300= 45+105+ handshakes btw b&g
Required handshake= handshakes btw boys n girls = 300-150=150

Hence D

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JoeKan1234
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In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   26 Mar 2024, 21:18
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Let b = number of boys, g = number of girls

bC2=105
b = 15

gC2 = 45
g = 10

Total number of ways to shake hands between a boy and a girl = Select a boy, then match him to a girl by selecting a girl

This means...

Number of ways to select a boy = 15C1 = 15
Number of ways to select a girl = 10C1 = 10

Total number of ways for the matching = 15*10 = 150
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In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   28 Mar 2024, 12:52
JerryAtDreamScore wrote:
Bunuel wrote:
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?

A. 15
B. 24
C. 25
D. 150
E. 300


Breaking Down the Info:

First, we need to find the number of handshakes made with n people.

Each person should handshake each other person (n - 1 people). Repeat this for all n people so that would be \(n*(n - 1)\) handshakes in total. The flaw with this method is that it double counts A shaking with B then B shaking with A, so we must divide that by 2 to get the real number of handshakes, which is \(\frac{n*(n - 1)}{2}\).

Now we may set \(\frac{n*(n - 1)}{2} = 45 \text{ or } 105\) to find \(n = 10\) or \(n = 15\) (10*9= 90 and 15*14 = 210).

Thus there are 25 students in the class, and plugging this in the formula gives \(25*12 = 300\).

Answer: E



This answer determines the total number of handshakes, including the 150 already accounted for boys-boys,girls-girls.

Subtracting the 150 from 300 yields 150 boy-girl handshakes.

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Re: In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink] New post   30 Mar 2024, 03:35
Bunuel wrote:
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?

A. 15
B. 24
C. 25
D. 150
E. 300



Assuming G girl student ,there will be Gc2 handshake among girls: G(G-1)/2=45...G=10.
Now if there are B boys,then there will be Bc2 handshake among boys: B(B-1)/2=105....B=15.
So each girl will handshake with 15 boys .Thus for 10 girls there will 150 handshake with boys..
Thus answear is D

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Re: In a class comprising boys and girls, there were 45 hand shakes amongs [#permalink]
30 Mar 2024, 03:35
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