# Free e-GMAT Live Webinar! Master SC with 90% Accuracy

## A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people

##### This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

### A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people

by BTGmoderatorDC » Tue Mar 07, 2023 4:24 am

00:00

A

B

C

D

E

## Global Stats

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) 1/3 of the people surveyed said that they buy product P but not product Q.
(2) 1/2 of the people surveyed said that they buy product Q.

OA C

Source: GMAT Prep

### GMAT/MBA Expert

GMAT Instructor
Posts: 16202
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

### Re: A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people

by [email protected] » Sat Mar 11, 2023 8:00 am

00:00

A

B

C

D

E

## Global Stats

BTGmoderatorDC wrote:
Tue Mar 07, 2023 4:24 am
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) 1/3 of the people surveyed said that they buy product P but not product Q.
(2) 1/2 of the people surveyed said that they buy product Q.

OA C

Source: GMAT Prep
This is a great candidate for a technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
When I scan the two statements I see that they mention 1/3 of the people surveyed and 1/2 of the people surveyed. I also see that the target question asks us to find a fraction of the people surveyed (not the actual number). So, let's pick a nice number that works well with 1/3 and 1/2.
Let's say there 12 people were surveyed.

So, we'll start by setting up our diagram like this:

We want to find the fraction of the people surveyed said that they neither buy product P nor product Q. So, to answer this question, we need to know the number of people in the bottom right box (where the happy face is).

We're now ready to check the statements.

Statement 1: 1/3 of the people surveyed said that they buy product P but not product Q.
1/3 of 12 = 4. So, 4 people buy product P but not product Q.

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 1 is NOT SUFFICIENT

Statement 2: 1/2 of the people surveyed said that they buy product Q.
So, 6 people buy product Q, which means 6 people do not buy product Q

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We get:

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
YES.

Since the two boxed in the right-hand column must add to 6, the bottom right box must have 2 people, which means 2/12 people said that they neither buy product P nor product Q.

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT