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.

DumplingBoy · Answer

Am I ill or is there no a,b,c,d,e options shown?

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are  always the same  and usually  omitted on the site .

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

SwiftMonk · Answer

please go through question types asked in gmat.
this a DS question part of DI.

DumplingBoy · Answer

Apologies I've not been practicing DS yet, but came across this one from the daily mailing list, hence the confusion. Thanks for taking the time to share!

Bunuel · Answer

No problem at all! I’d just suggest getting familiar with the standard DS answer choices, as knowing them by heart will make these questions easier to work with.

SwiftMonk · Answer

best method is the use of venn diagram.
thanks,it was really helpful

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

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

	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

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards