Problem Solving

Hello,

Can you please assist with this:

People who live in a certain apartment building subscribe only to magazines Q, R,
or S. Forty-five people live in the building and 39 people subscribe to at least one
magazine. Sixteen people subscribe to magazine Q, 19 people subscribe to
magazine R, and 22 people subscribe to magazine S. Eight people subscribe to
magazines Q and R, 7 people subscribe to magazines R and S, and 9 people subscribe
to magazines S and Q. The number of people who subscribe to the three magazines
equals the number of people who subscribe to none. How many people in the building
subscribe to only one magazine?

OA: 27


I tried to solve as follows:

a + b + c + d + e + f + g = 39

a + d + e + g = 16
b + d + f + g = 19
c + e + f + g = 22

a + b + d + e + f + g = 8
b + c + d + e + f + g = 7
a + c + d + e + f + g = 9

g = 45 - 39 = 6

a + b + c = ?


From above we have,

a + b + c + 2d + 2e + 2f + 3g = 57 - Eq. 1

2a + 2b + 2c + 3d + 3e + 3f + 3g = 24 - Eq. 2

a + b + c + d + e + f + g = 39 - Eq. 3


I was just wondering if this approach is correct since I get a negative answer when I solve the above 3 equations. Can you please assist?

Thanks,
Sri

gmattesttaker2 wrote:Hello,

Can you please assist with this:

People who live in a certain apartment building subscribe only to magazines Q, R,
or S. Forty-five people live in the building and 39 people subscribe to at least one
magazine. Sixteen people subscribe to magazine Q, 19 people subscribe to
magazine R, and 22 people subscribe to magazine S. Eight people subscribe to
magazines Q and R, 7 people subscribe to magazines R and S, and 9 people subscribe
to magazines S and Q. The number of people who subscribe to the three magazines
equals the number of people who subscribe to none. How many people in the building
subscribe to only one magazine?

OA: 27

Since 39 of the 45 people subscribe to at least one magazine, the number who subscribe to none = 45-39 = 6.
Since the number who subscribe to all 3 magazines is equal to the number who subscribe to none:
All 3 = none = 6.

Draw a VENN DIAGRAM representing the following:
T = 45
Q = 16
R = 19
S = 22
QRS = 6
N = 6.


Complete the Venn diagram by working from the INSIDE OUT.

Eight people subscribe to magazines Q and R.
7 people subscribe to magazines R and S.
9 people subscribe to magazines S and Q.
Subtracting from these figures the 6 who subscribe to all 3 magazines, we get:


Subtracting the values in the circles from Q=16, R=19, and Q=22, we get:


Thus:
Only Q + Only R + Only S = 5 + 10 + 12 = 27.

For a similar problem, check here:

https://www.beatthegmat.com/percentage-t270130.html