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

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emranhstu
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There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   Updated on: 09 Aug 2015, 02:28
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80% (02:14) correct 20% (02:32) wrong based on 418 sessions
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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
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Official Answer
D

Originally posted by emranhstu on 08 Aug 2015, 23:08.
Last edited by Bunuel on 09 Aug 2015, 02:28, edited 1 time in total.
RENAMED THE TOPIC.
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   09 Aug 2015, 11:16
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emranhstu wrote:
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


We have to find the value of the shaded region.
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   09 Aug 2015, 02:41
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emranhstu wrote:
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

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
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There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   26 Feb 2016, 20:39
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.?
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   26 Feb 2016, 21:04
mahakmalik wrote:
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.?


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.

Attachment:
2016-02-26_22-45-45.jpg
2016-02-26_22-45-45.jpg [ 17.03 KiB | Viewed 8474 times ]


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.
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   27 Feb 2016, 00:22
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mahakmalik wrote:
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.?


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
Quote:
formula for exactly two is:-

total=A+B+C-(sum of two groups)-2(all three)+neither(if A ,B and C stand for not ONLY but ALL)
otherwise in context of the Q
total=A+B+C+(sum of only two groups)+(all three)
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)+6
total snakes= s+x+y+6..
49-30=s+x+y+6
{s+x+y+6}=19..
19 is the answer


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
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   27 Feb 2016, 04:20
chetan2u wrote:
mahakmalik wrote:
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.?


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
Quote:
formula for exactly two is:-

total=A+B+C-(sum of two groups)-2(all three)+neither(if A ,B and C stand for not ONLY but ALL)
otherwise in context of the Q
total=A+B+C+(sum of only two groups)+(all three)
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)+6
total snakes= s+x+y+6..
49-30=s+x+y+6
{s+x+y+6}=19..
19 is the answer


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


Thankyou. i understand my mistake now..........
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   12 Mar 2021, 01:47
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emranhstu wrote:
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


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
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink] New post   24 Sep 2023, 04:30
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Re: There are 49 people that own pets. 15 people own only dogs, 10 people [#permalink]
24 Sep 2023, 04:30
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