GMAT Math

A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people surveyed said that they buy neither product P nor product Q?

1. one third of the people surveyed said that they buy product P but not product Q

2. one half of the people surveyed said that they buy product Q

OA: C

This is set theory question.Unfortunately,I can't draw the Venn diagram,but I will try to explain as lucidly as I can.

Let P= only product P
Q= only product Q
x = both P and Q
N = neither P nor Q

Total no of people = P+Q+x+N

We are asked what is N/(P+Q+x+N)=? or N/T=?

1) For simplicity assume T=30 (because it is easily divisible by 10)

P=10

We are given no info about Q and x(we need this info to find N).Therefore, we can't find the ratio.

Hence insufficient.Eliminate A and D

2) T=30

Q+x=1/2(30)=15 (reason because the statement does not say Q but not P,as in 1)

Again Insufficient because we need P to find N.P could be anything.

Eliminate B

Combining 1 and 2

P=10 from 1 and Q+x=15 from 2

Therefore N=5

Ratio =5/30=1/6

Sufficient Answer is C

Alternatively, you could also have used algebra.

Let T=a

1) p=a/3

Ratio = N/a ( we don't know what fraction of total people is Q+x)

Insufficient

2) similarly 2 is insufficient

from 1 and 2

P=a/3

Q+x=a/2

N= a-a/2-a/3= 1/6a(6-3-2)=1/6a
T=a

N/T= 1/6

What is the OA?