Around the World in 80 Questions (Day 4): Of the retailers surveyed

Question

Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?

(1) 15 percent of the retailers owned an online store but not a physical store.

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.

Bunuel · Accepted Answer

Official Solution:

Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?

From the question:

• {Online} = 65.

• {Physical} = 75.

We want: physical store but not online store, so {Physical only}.

(1) 15 percent of the retailers owned an online store but not a physical store.

{Online only} = 15.

Since {Online} = 65, then {Both} = 65 - 15 = 50.

Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.

Sufficient.

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.

This implies: {Both} = 5 * {Neither}.

{Total} = {Online} + {Physical} - {Both} + {Neither}

100 = 65 + 75 - 5 * {Neither} + {Neither}

{Neither} = 10, and thus {Both} = 5 * {Neither} = 50.

Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.

Sufficient.

Answer: D

NiranjanaV · Answer

Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?

(1) 15 percent of the retailers owned an online store but not a physical store.
=> Neither online nor physical stores = Total (no physical) - (yes online but no physical) = 25% - 15% = 10% 
Q: 35% - 10% ----> SUFFICIENT

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
=> Both = 5(neither)
=> Let owned a physical store but did not own an online store be 'y'
=> 75% - 5x = 35% - x
=> 4x = 40% => x = 10%
=> y = 35% - 10% ---> SUFFICIENT

Answer -

KanikaJain · Answer

Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?

(1) 15 percent of the retailers owned an online store but not a physical store.

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.

Online = 65%
Physical = 75%
Case I:
15% owned online but not physical
Thus owning both = 65 – 15 = 50%
And owning only physical = 75 – 50% = 25%

Case II:
Online + physical = 5* none
None = x
Thus 65 + 75 + x – 5x = 100%
Thus x = 50% and percent owning only physical = 25%

Thus D - both are sufficient

Kinshook · Answer

Given: Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. 
Asked: What percent of the retailers owned a physical store but did not own an online store?

Online Store  Not Online Store  Total  
  Offline Store      75%  
  Not Offline Store      25%  
  Total  65%  35%  100%

(1) 15 percent of the retailers owned an online store but not a physical store.
 
    Online Store  Not Online Store  Total  
  Offline Store  65%-15%=50%  75%-50%=25%  75%  
  Not Offline Store  15%  25%-15%=10%  25%  
  Total  65%  35%  100%  
 
The percent of the retailers owned a physical store but did not own an online store = 25%
SUFFICIENT

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.

Online Store  Not Online Store  Total  
  Offline Store  5x  75%-5x=35%-x  75%  
  Not Offline Store    x  25%  
  Total  65%  35%  100%

75%-5x = 35%-x 
4x = 40%
x =10%

Online Store  Not Online Store  Total  
  Offline Store  50%  25%  75%  
  Not Offline Store  15%  10%  25%  
  Total  65%  35%  100%

The percent of the retailers owned a physical store but did not own an online store = 25%
SUFFICIENT

IMO D

missionmba2025 · Answer

we can use table or overlapping set to solve this question. I will use table. We have to find the yellow cell.

(1) 15 percent of the retailers owned an online store but not a physical store.

As we know that 15% is the overlap between online and the physical store. The percentage of the overlap (yellow region) is 65-15 = 50.

Sufficient.

(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.

Let the percentage of neither = x.

Using the table shown we can find that 75 - 5x + x = 35

We will have an unique value. Hence, this information is also sufficient.

https://i.ibb.co/LxbCD1t/DSQ2.jpg

IMO D

TargetKellogg2024 · Answer

walterwhite756 · Answer

let S1 = retailers who owned only online store, S2 = owned both stores, S3 = owned physical store.
Also S1+S2 = 65, S2+S3 = 75

(1) S1 = 15.
So S2 and S3 can be found. Sufficient.

(2) Let none = x.
So S2 = 5x.
S1 = 65-5x and S3 = 75-5x, total = 100 so x can be solved. Sufficient.

IMO D.

Around the World in 80 Questions (Day 4): Of the retailers surveyed

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	Online Store	Not Online Store	Total
Offline Store			75%
Not Offline Store			25%
Total	65%	35%	100%

GMAT Data Sufficiency (DS) Questions

Around the World in 80 Questions (Day 4): Of the retailers surveyed

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

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My Rewards