Retailers question

Question

Q. 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.

OA: E

But i am getting C.
Here is the way i did it.
Let CB - Retailers who purchased computers for business purposes.
S - Retailers who own stores.
T - Total number of retailers surveyed.
We need to find [CB/T]

ST 1: 0.85S = CB

ST 2: 0.4T = S

Hence, when the 2 statements are combined.
CB/T = 0.85S/ (S/0.4); CB/T = 0.85(0.4)

Can someone please point out the error in this?

Turnpike · Answer

First let me go with option 'C' and see what the result is.

let the total number of retailers surveyed be 100.

(2) tells us that 40 of them own their own stores
(1) tells us that 85% of those 40 (who own their own stores) purchased computers. that's 34 retailers.

so u think you got the answer?

no, you didn't

read the question again. just the question.

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

is it asking you the percentage of those retailers who own their stores?

no, it isn't.

It's asking you about ALL the retailers!!!

that's not just the 40 of those who own their stores, but also the other 60 who don't.

the 34 are those who own their stores and have bought computers. we don't know how many, if at all, of those who don't own their stores bought computers.

so the answer is E.

it's a great question. not so much quant aptitude as it is about understanding what's been asked for.

thanks for sharing

good luck.

ben wade · Answer

Thanks for the reply turnpike.
The source of this question is the Diag test of OG 12. After looking at the OG explanation, I sort of figured my mistake. But i wanted to confirm whether that understanding was correct.

Your clear answer resolved it for me. Thanks once again.
This question is a good example of the GMAT traps.

Rich.C@EMPOWERgmat.com · Answer

Hi All,

We're asked - in a survey of retailers, what percent had purchased computers for business purposes. This question can be solved with a bit of logic (and no real math is needed).

1) 85 percent of the retailers surveyed who OWNED THEIR OWN STORE had purchased computers for business purposes.

Fact 1 introduces the idea that there are at two types of retails - those who own their own store and those who don't. The information in Fact 1 only gives us information on one of the two groups - and does not tell us anything about the number of of retailers in each group.
Fact 1 is INSUFFICIENT

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

Fact 2 also introduces the idea that there are at two types of retails - those who own their own store and those who don't. The information in Fact 2 only gives us information on the percent of retailers who own their own store, but tells us nothing about whether those owners purchased computers for business purposes or not.
Fact 2 is INSUFFICIENT

Combined, we know:
40 percent of the retailers surveyed owned their own store.
85 percent of the retailers surveyed who OWNED THEIR OWN STORE had purchased computers for business purposes.

With this information, we still don't know anything about retailers who do NOT own their own stories, so there's no way to answer the given question.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

ceilidh.erickson · Answer

ben wade wrote:Q. 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.

OA: E

But i am getting C.
Here is the way i did it.
Let CB - Retailers who purchased computers for business purposes.
S - Retailers who own stores.
T - Total number of retailers surveyed.
We need to find [CB/T]

ST 1: 0.85S = CB

ST 2: 0.4T = S

Hence, when the 2 statements are combined.
CB/T = 0.85S/ (S/0.4); CB/T = 0.85(0.4)

Can someone please point out the error in this?

One way to easily see your error is to use a Double Set Matrix.

Here, retailers either owned their own store or they didn't; they either purchased a computer for business purposes or they didn't:

I've circled the box that represents our target question: % of retailers who purchased a computer for business purposes, total. We can represent the overall total as 100.

When you fill in the information from the statements, keep careful track of what you learned from each statement v. what you know from the question stem.

(1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes.
This is 85% of an unknown total who owned their own store:

We clearly won't get a value for our target box. Insufficient.

(2) 40 percent of the retailers surveyed owned their own store.
First, erase what you knew from statement 1 and evaluate this statement on its own:

This won't get us a value for our target box. Insufficient.

(1) & (2) together:
Put all of the information into the matrix and make all possible inferences:

We see here that we still won't get a value for our target box. Insufficient.

The answer is E.

For more on using Double Set Matrices, see:
https://www.beatthegmat.com/rainbow-tro ... tml#555603
https://www.beatthegmat.com/survery-res ... tml#576105
https://www.beatthegmat.com/ds-question ... tml#677080
https://www.beatthegmat.com/sandwich-t2 ... tml#730500
https://www.beatthegmat.com/jefferson-s ... tml#708717
https://www.beatthegmat.com/in-a-class- ... tml#802582

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Brent@GMATPrepNow · Answer

Brent Hanneson - Creator of GMATPrepNow.com

Jeff@TargetTestPrep · Answer

ben wade wrote:Q. 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.

Statement One Alone:

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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