In a survey of retailers, what percent had purchased computers for bus

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:


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

Answer: E.


_________________

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.

Thus, Answer is (E).

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

Dear cyberjadugar,
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,

The question is asking what percent had purchased computers for business purposes?

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!

Regards,

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.

Answer E

Here's another way of doing this:



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.

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...............
_________________

Somehow I am not getting to the solution of this one

The question says "what percent had purchased
computers for business purposes?"

=> 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.

Plz Advice

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

what percent had purchased computers for business purposes?

Here percent should be of TOTAL and NOT YELLOW

Plz Advice

Rgds,
TGC

Yellow box IS total for computers purchased for business purposes.
_________________

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.
Please check the matrix below.

_________________

Here is a visual that should help.

Hi Bunuel,

How long should a question like this take to answer? I a atleast consuming 2-3 minutes on a questions like this.

Abhinav

As you can see in timers' stats, average time users took to answer this question correctly is 02:06. So, ~2 minutes should be OK.
_________________

85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes.

Since we don’t know the number of retailers who don’t own their own stores and the percentage of those retailers who purchased computers for business purposes, statement one is not sufficient to answer the question.

Statement Two Alone:

40 percent of the retailers surveyed owned their own store.

Since statement two tells us nothing regarding the retailers who purchased their computer for business purposes, statement two alone does not answer the question.

Statements One and Two Together:

With both statements, although we know the percentage of the retailers who don’t own their stores, we still don’t know the percentage of those retailers who purchased computers for business purposes. The two statements together are not sufficient to answer the question.

Answer: E
_________________

Answer - E

Reason - Statement one tells us that of the people surveyed, few had their own store, and of those people, 85% purchased computers for business purposes. To put it in mathematical form - there were x% people from total who owned a store, and of that x%, 85% purchased computers for business. So, in this statement, 2 things are missing, 1 what is x over here, and other than the X%, how many other people had bought computers for business? Hence A, and D were eliminated.

Statement 2 tells us that 40% of people owned their store. Definitely not sufficient. B eliminated.

Combining the statements, We still are missing one major piece of information and that is other than the 40% of people who owned their own store, were there any other people who also bought computers for business purposes? Hence E is the answer.