5 Indian & 5 American Couples Meet At A Party And Shake Hands GMAT Problem-Solving

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.

Total people = (5 * 2) plus (5 * 2), which is 20.
There are nC2 = 20C2 = 190 potential handshakes in all.

The handshakes that never took place:

The total number of couples is equal to the number of wives shaking hands with their own husbands: 10.
Number of Indian wives * Number of other males = 5 * 9 = 45 Handshakes of Indian wives with males (other than their own husbands, since that is already counted above)
As a result, the actual number of handshakes was (190 - 10 - 45) = 135

C is the correct answer.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.

10 multiplied by 2 equals a total of 20 persons.
The maximum number of handshakes is 20C2 = (20*19)/2 = 190.

NO handshakes allowed
1) Indian women refrain from shaking hands with all men, even their own husbands = 5C1 ∗ 10C1 = 5∗10 = 50
2) American wives do not shake hands with their own husbands, therefore, there are five couples.
Total handshakes inside the boundaries given: 190- 50 - 5=135

C is the correct answer.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.

good cases l all potential cases - bad instances.

All potential scenarios
The number of possibilities to establish a pair to shake hands from 20 persons is 20C2 =20*19/2 = 190

Bad example 1: A man shakes hands with an Indian woman
There are five different approaches to pick an Indian woman.
There are 10 different ways to pick a man.
We multiply these choices to combine them:
5*10 = 50

Bad example 2: A woman from America shakes hands with her own husband
Five American marriages could result in a lady shaking hands with her own husband, therefore we get:
As a result, good cases equal all scenarios. (Worst case scenario) - (Worst case scenario) = 190 - 50 - 5 = 135

The appropriate answer is C.