Difficult Math Problem #103 - Sets

[800guy]

Out of 20 surveyed students 8 study math and 7
study both math and physics. If 10 students do not
study either of these subjects, how many students
study physics but not math?

(A) 1
(B) 2
(C) 4
(D) 5
(E) 6

from diff math doc. answer coming when some people respond with explanations

[Neo2000]

Look at the attached image.
Number of people studying both M & P = 7
Number studying ONLY M = 1
Number NOT studying any subject = 10
Therefore total number of students studying ONLY P = 20 -(10+1+7) = 2


p.s. Can someone show me how to insert an image directly into the post ??

[beatthegmat]

Hi Neo:

There isn't an easy way to insert images directly within posts. You have two options:

1. Upload image as attachment, which will be viewable to members
2. Host the image on another website and link to that image here (this will make the image appear embedded within the post)

Thanks!

[Neo2000]

Thanks Eric.

I was actually aiming for option 1 itself. My experience on other forums is that an attached image is usually shown at the bottom of the post but here its nice, big and bold

[beatthegmat]

I'm happy you like our style here, Neo.

[800guy]

here's the OA:

total = gr1 + gr2 - both + neither
20 = 8 + P - 7 + 10
P = 9, 9 students study both P and M, 7 study both, 9-7 = 2 study only P

[BTGmoderatorRO]

we can solve this using Venn diagram,
let M represent Mathematics and P denotes Physics
total number of students=20
number of students that study M and P= 7
number of students that do not study M nor P= 10
number students that study only M=8-7=1
number students that study only P = 20 - (10 + 1 + 7 ) =2

option B is correct

[Scott@TargetTestPrep]

Out of 20 surveyed students 8 study math and 7
study both math and physics. If 10 students do not
study either of these subjects, how many students
study physics but not math?

(A) 1
(B) 2
(C) 4
(D) 5
(E) 6

from diff math doc. answer coming when some people respond with explanations

We can use the formula:

Total = Math + Physics - Both + Neither

So we have:

20 = 8 + P - 7 + 10

20 = 11 + P

9 = P

Since the 9 people studying Physics include the 7 people who also study Math, the number of people who study Physics only is 9 - 7 = 2.

Answer: B