In an IT company, there are a total of 110 employees including 50

Hi RudeyboyZ,

The question tells us about a company where the employees are either programmers or non-programmers. We are asked to find the minimum no. of employees that needs to be picked to ensure that we have either 3 male programmers or 3 female programmers.

I am putting up a diagram to help you understand the question better:



We are given in the question that there are 110 employees and 50 programmers. That would leave us with 60 non-programmers. Out of the 50 programmers we have 35 male programmers and the balance 15 as female programmers.

The question asks us the minimum no. of employees that must be selected to guaranty that we have 3 programmers of the same sex i.e. either 3 male programmers or 3 female programmers.

Since the question is asking to guaranty picking up of 3 programmers of same sex, that would mean we need to exhaust all the possibility of picking up the non-programmers and then start picking up the programmers.That can only be done if we pick all the non-programmers first and then start picking up the programmers.

So we can pick all the 60 non-programmers.

Since we are left with only programmers now, we can start picking them up. Picking up 3 programmers would not guaranty us 3 same sex programmers as there may be 2 male programmers and 1 female programmers. Similarly picking up 4 programmers may leave us with 2 male programmers and 2 female programmers.

Picking any one of the more programmers would give us 3 programmers of same sex. So we need to pick up a minimum of 60 + 4 + 1 = 65 employees to ensure that we have 3 programmers of the same sex.

Hope it's clear

Regards
Harsh
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You could pick 60 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 65.

Amazing explanation. Thanks for your expertise!

I don't think I understand the question, will you please help me understand the question better.
thanks and regards,

Rudey!

Dear Harsh,

Thank you for the explanation, it has really opened up my mind to understanding the logic behind questions like this.

Do we get questions like the one above on the gmat, if so, how many can one expect? and what is the difficulty level of these questions, assuming now that I know how to solve this, it looks easy.

Warm Regards,

Rudey!

Hi RudeyboyZ,

Questions such as these are expected on the GMAT. Around 10%-15% of the OG questions are based on such concepts and can be solved using the tree structure diagram. This question is at best of medium difficulty level. .

Questions where you have multiple data points which have a dependency among them, try to represent it pictorially. Pictorial representation helps in better visualization of the information given as well as the question asked.

You may also try out the following question for your practice:
https://gmatclub.com/forum/according-to-a-certain-estimation-the-total-number-of-black-cats-is-198573.html

Once you feel confident in solving such questions give an attempt on these 3 700+ level questions on sets
https://gmatclub.com/forum/the-e-gmat-sets-triad-3-exciting-sets-questions-198192.html

Hope this helps

Regards
Harsh
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Dear Harsh,

Valuable information provided, my deepest thanks.

Warm Regards,

Rudraksh

Check other Worst Case Scenario Questions from our Special Questions Directory.
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total employee = 100
Programmer= 50 and male = 35 , Female= 15
Non programer= 60
now to have 3 programmers of same sex ; remove all non programmers i.e 60 and so left with 50 Programmers ; out of which to get a multiple of 3 we need to remove 5 of programmers ; left with 45 so total 60+5 ; 65 to be selected
IMO E

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