In a survey of retailers, what percent had purchased : GMAT Data Sufficiency (DS)
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# In a survey of retailers, what percent had purchased

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14 Jun 2012, 02:17
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In a survey of retailers, what percent had purchased computers for business purposes?

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes.
(2) 40 percent of the retailers surveyed owned their own store.

Diagnostic Test
Question: 29
Page: 25
Difficulty: 650
[Reveal] Spoiler: OA

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14 Jun 2012, 02:17
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In a survey of retailers, what percent had purchased computers for business purposes?

Say there are total of 100 retailers.

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes. Clearly insufficient, since we don't know how many retailers own their store and also how many retailers who do NOT own a store had purchased computers for business purposes. Not sufficient.

(2) 40 percent of the retailers surveyed owned their own store. Clearly insufficient.

(1)+(2) From (2) we can answer the first question, we had in (1) but not the second question: we still don't know how many retailers who do NOT own a store had purchased computers for business purposes. Not sufficient.

To elaborate more consider the diagram below:

As you can see we can not find the value of X from the info provided.

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14 Jun 2012, 04:41
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In a survey of retailers, what percent had purchased computers for business purposes?

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes.
(2) 40 percent of the retailers surveyed owned their own store.
Hi,

From (1),
85% of the retailers surveyed who owned their own store had purchased computers for business purposes.

From (2)
40% of the retailers surveyed owned their own store.

Using both (1) & (2),
People who owned their own store had purchased computers for business purposes = 0.4*0.85 = 0.34
but this fraction is from those who own store. No information is given about the people who don't own the store.

It could be better explained using the diagram: (x is a variable & I think you could get the meaning of grey area, )
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Comp.jpg [ 14.62 KiB | Viewed 14651 times ]

Last edited by cyberjadugar on 09 Jul 2012, 00:03, edited 1 time in total.
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14 Jun 2012, 06:51
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Hi,

From (1),
85% of the retailers surveyed who owned their own store had purchased computers for business purposes.

From (2)
40% of the retailers surveyed owned their own store.

Using both (1) & (2),
People who owned their own store had purchased computers for business purposes = 0.4*0.85 = 0.34
but this fraction is from those who own store. No information is given about the people who don't own the store.

It could be better explained using the diagram: (x is a variable & I think you could get the meaning of grey area, )

cud u pls explain why are we considering who own stores and who do not. the question is not asking for it.
it seems i am not getting an imp point.
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14 Jun 2012, 07:06
kashishh wrote:
cud u pls explain why are we considering who own stores and who do not. the question is not asking for it.
it seems i am not getting an imp point.

Hi,

and on solving we get,
People who owned their own store had purchased computers for business purposes = 0.4*0.85 = 0.34 or 34%

I can't surely say that there are no more people other than those who own stores, and this is perhaps questionable!

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16 Jun 2012, 04:03
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Difficulty level: 650 only because of language

Important: Need to calculate the percentage of people who bought computers for business purpose.

Stmt 1: 85% of retailers surveyed who owned their own store had purchased computers for business purpose: There is possibility of retailers didnt owning a store still have bought computer for business purpose. Insufficient.

Stmt 2: 40% of the retailers surveyed owned their own store: This allows us to calculate the percentage of retailers who owned their own store and who didnt own their own store but we do not know how many of them purchased computers for business purpose. Insufficient.

Together: We know the percentage of retailers who owned store and also bought computer for business purpose but we can not calculate the percentage of people who didnt own store but still bought computer for business purpose. Both together insufficient.

Catch is in the last portion which makes this question difficult to answer under pressure.

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18 Jun 2012, 08:26
sanjoo wrote:
y is it seems like it is A..

BUT i THINK m WRONG...

bunuel ...can u explain it..

Hi,

While, what is given in the option (A) is the subset (those who own store had purchased computers) of all the surveyed retailer and there is no info about the other retailers who do not own any store (they might have purchased computer for business purposes).

Thus, the information given in the statements is insufficient.

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18 Jun 2012, 08:53
Here's another way of doing this:

Attachment:

Capture.JPG [ 31.58 KiB | Viewed 14353 times ]

N is the total number of survey participants including those who own their own stores and those who do not.
Both statements together are insufficient because we are not given any information on how many store owners who took part in the survey and who do not own their store purchased computers. Statement 2 states that 40 percent of the retailers surveyed owned their own store; therefore logically the other 60 percent consists of retailers who do not own their own store.

I usually prefer doing overlapping sets type questions using tables a la MGMAT style. Others may find this approach helpful as well.
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22 Jun 2012, 03:25
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SOLUTION

In a survey of retailers, what percent had purchased computers for business purposes?

Say there are total of 100 retailers.

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes. Clearly insufficient, since we don't know how many retailers own their store and also how many retailers who do NOT own a store had purchased computers for business purposes. Not sufficient.

(2) 40 percent of the retailers surveyed owned their own store. Clearly insufficient.

(1)+(2) From (2) we can answer the first question, we had in (1) but not the second question: we still don't know how many retailers who do NOT own a store had purchased computers for business purposes. Not sufficient.

To elaborate more consider the diagram below:
Attachment:

Retailers.png [ 8.47 KiB | Viewed 15315 times ]
As you can see we can not find the value of X from the info provided.

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22 Jun 2012, 05:05
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This question in my opinion is more or less 600.

using only logic we obtain E.

1) 80 % of what number 10 retailer or 1 million ?'

2) 40% of the retailers surveyed owned their own store.

1) + 2) here we have only % of what real number to manipulate ?? Not enough...............
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26 Feb 2013, 01:49
I fail because I am cheated.

not easy. cheating is the game on math.

caution.

I want to follow this posting.
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23 Mar 2013, 09:43
Somehow I am not getting to the solution of this one

The question says "what percent had purchased

=> What percent OF TOTAL purchased computer for BUSINESS PURPOSES?

As calculated by BUNUEL, the answer is 34% .

So, isn't (C) should be the answer.

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24 Mar 2013, 02:49
targetgmatchotu wrote:
Somehow I am not getting to the solution of this one

The question says "what percent had purchased

=> What percent OF TOTAL purchased computer for BUSINESS PURPOSES?

As calculated by BUNUEL, the answer is 34% .

So, isn't (C) should be the answer.

Rgds,
TGC

We need to find what percent had purchased computers for business purposes, which is yellow box here: in-a-survey-of-retailers-what-percent-had-purchased-134506.html#p1098581 and it cannot be found.

34% is % of the retailers who owned their own store and purchased computers for business purposes.

Hope it helps.
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24 Mar 2013, 07:58
Bunuel wrote:
targetgmatchotu wrote:
Somehow I am not getting to the solution of this one

The question says "what percent had purchased

=> What percent OF TOTAL purchased computer for BUSINESS PURPOSES?

As calculated by BUNUEL, the answer is 34% .

So, isn't (C) should be the answer.

Rgds,
TGC

We need to find what percent had purchased computers for business purposes, which is yellow box here: in-a-survey-of-retailers-what-percent-had-purchased-134506.html#p1098581 and it cannot be found.

34% is % of the retailers who owned their own store and purchased computers for business purposes.

Hope it helps.

I might be wrong 100%,but still it is unclear to me

Here percent should be of TOTAL and NOT YELLOW

Rgds,
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25 Mar 2013, 04:02
targetgmatchotu wrote:
Bunuel wrote:
targetgmatchotu wrote:
Somehow I am not getting to the solution of this one

The question says "what percent had purchased

=> What percent OF TOTAL purchased computer for BUSINESS PURPOSES?

As calculated by BUNUEL, the answer is 34% .

So, isn't (C) should be the answer.

Rgds,
TGC

We need to find what percent had purchased computers for business purposes, which is yellow box here: in-a-survey-of-retailers-what-percent-had-purchased-134506.html#p1098581 and it cannot be found.

34% is % of the retailers who owned their own store and purchased computers for business purposes.

Hope it helps.

I might be wrong 100%,but still it is unclear to me

Here percent should be of TOTAL and NOT YELLOW

Rgds,
TGC

Yellow box IS total for computers purchased for business purposes.
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05 Jul 2013, 16:15
In a survey of retailers, what percent had purchased computers for business purposes?
(A) 85% of the retailers surveyed who owned their own store had purchased computers for business purposes.
(B) 40% of the retailers surveyed owned their own stores.
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06 Jul 2013, 00:06
SmitM wrote:
In a survey of retailers, what percent had purchased computers for business purposes?
(A) 85% of the retailers surveyed who owned their own store had purchased computers for business purposes.
(B) 40% of the retailers surveyed owned their own stores.

Merging similar topics. Refer to the solutions above and ask if anything remains unclear.

All OG13 questions to practice: the-official-guide-quantitative-question-directory-143450.html

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17 Dec 2013, 09:46
Bunuel wrote:
In a survey of retailers, what percent had purchased computers for business purposes?

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes.
(2) 40 percent of the retailers surveyed owned their own store.

Diagnostic Test
Question: 29
Page: 25
Difficulty: 650

Stm 1 only tells us stuff about people who own stores
stm 2 tells us how many in total are of the group in stmn1

we know nothing about those who do not own their own store and the question asks for traits of the total sample. So clearly E.
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24 Mar 2015, 09:49
Bunuel

In this question, why can't we derive the total of computer for biz purpose as follow:

If 40%x is number of retailers owning a store, then 60%x is number of retailers not owing a shop. Also, if 85%of 40%x is number of retailers owing a store and using computer for biz purpose, then 15%(given from 100%-85%)of 60%x is number of retailers not owing a store but using computer for biz purpose.

So 1)+2) 85/100*40/100*x+15/100*60/100*x= tot of retailers using computers for biz purpose. To me seems legit C.

Please, let me know why I'm wrong.
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24 Mar 2015, 11:17
elisabettaportioli wrote:
Bunuel

In this question, why can't we derive the total of computer for biz purpose as follow:

If 40%x is number of retailers owning a store, then 60%x is number of retailers not owing a shop. Also, if 85%of 40%x is number of retailers owing a store and using computer for biz purpose, then 15%(given from 100%-85%)of 60%x is number of retailers not owing a store but using computer for biz purpose.

So 1)+2) 85/100*40/100*x+15/100*60/100*x= tot of retailers using computers for biz purpose. To me seems legit C.

Please, let me know why I'm wrong.

The red part should be as follows: 15% of the retailers surveyed who owned their own store had NOT purchased computers for business purposes.

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Re: In a survey of retailers, what percent had purchased   [#permalink] 24 Mar 2015, 11:17

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