Data Sufficiency

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 they buy product P but not product Q

2) 1/2 of the people surveyed said that they buy Product Q.


[spoiler]OA: C. Please explain how to solve[/spoiler]

You could do it using Venn diagrams, here since the answer choices are straight forward let us choose numbers;

Assume total of 6 people are there;

Statement 1: 1/3rd (or) 2 people buy product P alone(No info about Q and others) Insufficient
Statement 2: 1/2 (or) 3 people buy Q (include people who buy both, but not sure of others)

Together you know 2 buy P alone and 3 buy Q (also includes those who buy both)

Hence people who do not buy either is 6-(2+3) = 1.

Hence C

sparkle6 wrote: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 they buy product P but not product Q

2) 1/2 of the people surveyed said that they buy Product Q.


[spoiler]OA: C. Please explain how to solve[/spoiler]

This problem can be solved using the two group formula

G1 + G2 - B + N = Total

G1 = only P + both
G2 = Only Q + both

So P + B + Q +B - B + N = total

Statement 1 - only info about P - no Q (insufficient)

Statement 2 - only info about B and B - no Q (insufficient)

1/2 + B + 1/3 - B + N = 1

the B's cancel out to get 5/6 + N = 1

N = 1/6

Because this is DS you don't have to solve, just get the formula to the point at which you can.

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