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## Retailers question

This topic has 3 expert replies and 2 member replies
ben wade Senior | Next Rank: 100 Posts
Joined
14 Jun 2009
Posted:
32 messages
1

#### Retailers question

Sun Aug 09, 2009 3:42 am
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?

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1778 messages
Followed by:
228 members
1443
Fri Feb 23, 2018 12:54 pm
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.

For more on using Double Set Matrices, see:
https://www.beatthegmat.com/rainbow-trout-vs-speckled-trout-t161101.html#555603
https://www.beatthegmat.com/survery-result-t176159.html#576105
https://www.beatthegmat.com/ds-question-need-help-t257565.html#677080
https://www.beatthegmat.com/sandwich-t279517.html#730500
https://www.beatthegmat.com/jefferson-school-t273638.html#708717
https://www.beatthegmat.com/in-a-class-of-200-students-forty-percent-are-girls-t298461.html#802582

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Manhattan Prep GMAT & GRE instructor
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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11403 messages
Followed by:
1229 members
5254
GMAT Score:
770
Fri Feb 23, 2018 2:22 pm
I thought I'd point out that Ceilidh's Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- owns store or doesn't own store
- purchased computers or did not purchase computers

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Once youâ€™re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/920
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/946
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/943
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- https://youtu.be/dOZ9KM1m5Hs
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
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Turnpike Senior | Next Rank: 100 Posts
Joined
08 Apr 2009
Posted:
56 messages
1
Test Date:
3rd Oct., 2009
Target GMAT Score:
730
GMAT Score:
700
Sun Aug 09, 2009 4:11 am
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.

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.

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 Senior | Next Rank: 100 Posts
Joined
14 Jun 2009
Posted:
32 messages
1
Sun Aug 09, 2009 4:21 am
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.

This question is a good example of the GMAT traps.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9301 messages
Followed by:
478 members
2867
GMAT Score:
800
Sun Feb 18, 2018 8:23 pm
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

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