There are 49 people that own pets. 15 people own only dogs, 10 people

Question

There are 49 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?

A 2
B 4
C 8
D 19
E 32

Subanta · Accepted Answer

We have to find the value of the shaded region.

D3N0 · Answer

Ans: D
lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 49
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x 
Exactly Cat and Snake = y
all three= 3

so 49=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 19

mahakmalik · Answer

formula for exactly two is:-

total=A+B+C-(sum of two groups)-2(all three)+neither
total=49
A=15
B=10
C=s
 a \bigcap b=5 
 b \bigcap s=x 
 s \bigcap a=y 
all three=6

49=15+10+s-(5+x+y)-2*6
49-13=s-5-x-y
36+5=s-x-y
41=s+x+y

could you tell me where am i wrong.?

ENGRTOMBA2018 · Answer

Couple of things: When you use variables without explaining as to what they stand for, is a big red flag. No one would know what variables stand for what function! Also, be consistent with your variables. If you use upper case variables, then continue with them. This question does not require that you memorize anything. Look at the attached image. 2016-02-26_22-45-45.jpg Based on the information given, a+b+c+d+e+f+g=49, g=15 a=10 e=5 d=3 the question asks us the value of b+d+e+f=? Thus, from the equations above, b+d+e+f=49-15-10-5=19 D is thus the correct answer. You do not have to go into the calculations of groups of 2 to arrive at the solution. Hope this helps.

chetan2u · Answer

Hi,
you have gone wrong in choosing the value of A, B and C..
these values 15 for A and 10 for B are ONLY CATS and ONLY DOGS..
whereas the equation you have formed is for ALL CATS and ALL dogs..
let me make changes to your solution

VeritasPrepKarishma , 
   NOTE:- The Q is not totally correct. We are talking in number of PEOPLE having pets and suddenly we have started asking for number of SNAKES..
number of snakes need not necessarily mean number of people having snake as pet..
it is nowhere mentioned each person has only one number of each pet

mahakmalik · Answer

Thankyou. i understand my mistake now..........

udaypratapsingh99 · Answer

Anyone who do not own any of only cats, only dogs, or only cats and dogs, own a combination that include snake.

Answer = 49-(15+5+10) = 19
Last statement, "3 people own cats, dogs and snakes" is a bait for confusion.

Correct answer is D

Karmoker · Answer

We can solve it using Venn Diagram easily

whatsinthename1 · Answer

Basically, if we take out people who do not have snakes from total people, we get people who do have snakes.

49-15-10-5=19

randomname4 · Answer

We need to be careful with the wording here. The question is asking for the total number of people who own snakes, not only the number of people who own all three pets.
There are 49 people total who own pets.
We are told:
Only dogs = 15
Only cats = 10
Only cats and dogs = 5
Cats, dogs, and snakes = 3
The people who definitely do  not  own snakes are:
15 + 10 + 5 = 30
So the remaining people must be snake owners:
49 - 30 = 19
This total includes the 3 people who own cats, dogs, and snakes, plus any people who own only snakes, dogs and snakes, or cats and snakes.
Therefore, the answer is  D. 19 .
Takeaway: In overlapping set questions, separate the groups that definitely do not belong to the category being asked about. Here, once we subtract all non-snake owners from the total, the remainder gives all snake owners.

There are 49 people that own pets. 15 people own only dogs, 10 people

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There are 49 people that own pets. 15 people own only dogs, 10 people

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