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In a class comprising boys and girls, there were 45 hand shakes amongs 20 Jan 2022, 08:49
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D
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65% (hard)

Question Stats:

57% (02:21) correct 43% (02:19) wrong based on 110 sessions

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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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D
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In a class comprising boys and girls, there were 45 hand shakes amongs 20 Jan 2022, 08:58
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Bunuel
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
Show more

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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In a class comprising boys and girls, there were 45 hand shakes amongs 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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In a class comprising boys and girls, there were 45 hand shakes amongs 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 28 Mar 2024, 12:52
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JerryAtDreamScore
Bunuel
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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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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In a class comprising boys and girls, there were 45 hand shakes amongs 30 Mar 2024, 03:35
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Bunuel
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
Show more


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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