Three competing juice makers conducted a blind taste test with mall

Question

Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?

A. 1,300
B. 1,000
C. 900
D. 700
E. 600

A. 1,300 
B. 1,000 
C. 900 
D. 700 
E. 600

Kurtosis · Answer

Given: Atleast 1 juice was liked by the participants. --> Neither = 0

Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets

I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(300) + 3*(50) = 1000
I = 250

Total number of shoppers who took the taste test = I + II + III = 250 + 300 + 50 = 600

Answer: E

Mohammad Ali Khan · Answer

could you please share the concept with me. It would be better to understand for me.

Vigasimrair · Answer

How it could be that 700 shoppers liked brand L and the total number of shoppers who took the taste test is 600?
Ghost shoppers?

jacobkeung · Answer

This is what I did.

Add J+K+L (100+200+700) = 1000
Then, deduct the shoppers that liked exactly 2 juices = 300
Then, deduct the shoppers that like all 3 (50) however you have to multiply this number by 2, as they have been counted twice in the singular (J+K+L) count.

100+200+700-300-100=600

Jawad001 · Answer

Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?

A. 1,300
B. 1,000
C. 900
D. 700
E. 600

A. 1,300
B. 1,000
C. 900
D. 700
E. 600

Solution:
Here,
A (Brand J) = 100
B (Brand K) = 200
C (Brand L) = 700

Exactly Two = 300
All three = 20

Neither = 0

**Formula
All = A + B + C – Sum of exactly two groups – 2*All Three + Neither
 = 100 + 200 + 700 – 300 -100 +0
 = 600
Answer:600(E)

jackfr2 · Answer

the question is wrong I think , as 300 shoppers like exactly 2 brands yet a+b-2*all 3=200
so there could only be 200 shoppers who liked exactly 2 brands . and how can 700 people like brand 3 if total shoppers is 600?

abannore · Answer

That 700 includes all who like brand L including people who like 2 brands and all 3 brands. This can be expressed using a Venn Diagram as shown in the attachment.

jackfr2 · Answer

the question is still wrong I think ? as there is only 600 people and why would you count 1 people twice is beyond me.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Three competing juice makers conducted a blind taste test with mall

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Three competing juice makers conducted a blind taste test with mall

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards