edited by
7,389 views
19 votes
19 votes

Among $150$ faculty members in an institute, $55$ are connected with each other through Facebook and $85$ are connected through Whatsapp. $30$ faculty members do not have Facebook or Whatsapp accounts. The numbers of faculty members connected only through Facebook accounts is _______.

  1. $35$
  2. $45$
  3. $65$
  4. $90$
edited by

5 Answers

Best answer
31 votes
31 votes
Let $F$ denotes Facebook users,

$W$ denotes Whatsapp users ,

$F'$  denotes those not using Facebook, and

$W'$ denotes those not using Whatsapp.

$U$ denotes universal set.

Total faculties in institute, $n(U)=150$

Facebook users, $n(F)=55$

Whatsapp users, $n(W)=85$

Faculty members not using Facebook or Whatsapp $n(F' \cap W')=30$

Faculty members using either Facebook or Whatsapp

$n(F\cup W)= n(U)-n(F' \cap W') =150-30=120$

Faculty members using both Facebook and Whatsapp

$n(F \cap W) =n(F) +n(W) - n(F\cup W) = 55+85-120= 20$

Faculty members using Facebook only

$n(F \cap W')= n(F)-n(F \cap W)= 55 -20 =35$
edited by
17 votes
17 votes
Always try to solve GATE aptitude part via common sense or via options. In most of the cases we don't really need any law or formula. And still using them just wastes out time.

Here, there are total 150 faculties. Out of them 30 don't have either Facebook or WhatsApp.

Therefore, remaining connected faculties are (150-30) = 120. Out of them 85 are connected via WhatsApp (may be they are even connected via Facebook but we don't care.)

So, number of faculties connected via ONLY Facebook is (120-85) = 35.
10 votes
10 votes
Here answer is A =>

Why ?

Total =150

FB => 55

Whatsapp => 85

30 people do not have FB or whatsapp => USE DEMORGANS LAW HERE !

now 30 people do (not have FB AND not have whatsapp)

~FB ^ ~Whatsapp = 30

People on FB or Whatsapp = 150 - 30 = 120

Now Consider option A

35 have only FB.

Then 55-35 => 20 Have both FB & Whatsapp.

Then only whatsapp guys are 85-20 = 65.

This sums up nicely

Only FB + Only WHatsapp + Both FB & Whatsapp => 35 + 65+ 20 =>120

Answer is A !
Answer:

Related questions

18 votes
18 votes
5 answers
2
22 votes
22 votes
5 answers
3
21 votes
21 votes
3 answers
4