Among the customers who bought either tables or chairs at a certain fu

We are given that the ratio of customers who bought tables to customers who bought chairs is 3:2. In other words, the ratio is 3x : 2x, in which 3x is the number of customers who bought tables and 2x is the number of customers who bought chairs. We are also given that half of those who bought chairs also bought tables. Thus (½)(2x) = x customers bought both chairs and tables, and hence, there is a total of 2x + 3x - x = 4x customers who bought one or both pieces of furniture. Since there are 3x customers who bought tables, the percentage of customers who bought tables is 3x/4x = ¾ = 75%.

Answer: D
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Lets say 6 people buy tables: 4 chairs. If half the people who bought chairs also bought tables, then 2 people bought chairs and tables. This means that 6 people bought tables, and Total # people= 6+4 -2 (to account for those that bought both) yields 8 people total. 6/8*100= 75%. D

lets say total was 100
so only table was 60 and only chair 40
half of chair buyers bought table also, so 20 of them
total table 80
thats 80%.

answer is E

But if now the total table buyers is 80, then it doesn't fit the 3:2 table:chair ratio any more, does it?
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Using set theory to solve this sum. Given the following

n(cust buying tables) = n(a) = 3x
n(cust buying chairs)=n(b)=2x.

We are asked to find n(A)/n(AuB).

n(AuB)=n(A)+n(B)-n(AnB)

Given n(AnB)=x - half of those who bought chairs also bought tables
n(AuB) = 3x+2x - x = 4x.

So ratio is 3x/4x = 75% - D

Cheers!

If the total was 100. Tables : Chair = 60 : 40 (3 : 2)

0.5 (40) = 20 buy tables.

\(=\frac{(40+20)}{(40+20+20)}*{100%}\)

\(={75%}\)

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As stated by Ron from MGMAT, it's very important to organize the data in some form or the other.
In this case, lets organize it in form of a table, as follows.
Ratio of Tables to Chairs inserted as 3a to 2a respectively.


-----------------------------Tables / Yes. -------Tables / No --------Total
Chairs / Yes.--------------a---------------------------a-----------------------2a
Chairs / No----------------2a----------------------- Nil----------------------2a
Total--------------------------3a-------------------------a-----------------------100

4a = 100 , means a = 25
Therefore, percent of Tables i.e. 3a = 75%. / Ans : Option D

Bunuel

Sir I have approached the problem in following way

Table/Toatal *100

\(\frac{x+x/2}{x+x/2+y}\)

Now using x/y=3/2 I'm getting 70%

What did I miss??

Hi

What you have done is x/y = 3/2. So you have taken the ratio of those people who bought Only Tables to those people who bought Only Chairs to be 3:2.

But that is NOT what is given in the question. The question says the ratio of People who bought Tables (these include those who bought chairs also along with tables) TO People who bought Chairs (these include those who bought tables also along with chairs) to be 3:2

So what you should do instead is (x + x/2)/(y + x/2) = 3/2. This will give you y=x/2, which you can then replace in the original venn diagram. Then number of customers with tables will become = x + x/2 = 3x/2. Number of customers with chairs will become = x/2 + x/2 = x. And Total customers = x + x/2 + x/2 = 2x

Therefore, percentage of people who bought tables = (3x/2)/(2x) * 100 = 75%

Hope this helps.

What is confusing here is the part in the problem statement "who bought either tables or chairs" is 3:2 but not both. I am sure most of us are confused here as I am when it comes to accepting the answer choice D as the correct answer.

Any comments?

The question doesn't specify in this statement that the customers bought ONLY tables or ONLY chairs. And without such specification the GMAT always assumes inclusivity. That is, "people who bought tables or chairs" means "people who bought tables or chairs OR BOTH" unless explicitly stated to the contrary.
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Tricky one!

1) Let's assume 40 people bought chairs.
2) Half of that is 20 (people who also bought tables).
Now 3:2 = (20+X)/40, solve for X (if you really need it), X = 40

3) So, total number of people is 40+40=80,
Number of people who bought tables is 60,

Percent 60/80=75%

The trick is to understand that the number of people who bough both chairs and tables is double counted in the ratio 3:2.
Thus, we can't say that if 40 people bought chairs and 60 bought tables than the total number of people was 100. It was 100-40/2=80!

Hope this helps!

While I understand that the intent of this question might be to force students to recognize the usage of "OR" as it pertains to set theory, I still think that the "either" in the sentence "among the customers who bought either tables or chairs" implies that the ratio is between customers who ONLY bought tables and those who ONLY bought chairs. For example if you're at a restaurant and the waiter tells you that along with your choice of dish, you can select "either soup or salad" as your side, that would necessarily mean that you can choose only soup or only salad, never both.

It seems unfair that this question punishes students who interpret the original ratio to mean ONLY tables or ONLY chairs. For example, the article linked states that "Either X or Y" means X or Y but not both (https://jakubmarian.com/both-vs-either-in-english/).
Bunuel

I disagree with your claim that



If I bought a table and a chair at a store and then someone asked me "did you buy either a table or a chair today?" I'd definitely say YES. So I basically just think your cited article is wrong, or at least making far too blanket a claim.

But putting this subjective interpretation disagreement aside, the standard convention in math is to interpret "or" inclusively unless otherwise noted.

The GMAT does not, to my knowledge, release a convention sheet. But the GRE does. The GRE's math convention sheet says, among other things,



and



https://www.ets.org/s/gre/pdf/gre_math_conventions.pdf

So, again, I just think you're reading this question wrong, and in any math question on the GMAT, GRE, SAT, ACT, or any other similar test, if you interpret "or" by default as "A or B but not both," then you're going to get wrong answers.

Bonus: The numbers in this question don't work at all and don't make any sense if the word "or" is interpreted as "A or B but not both." A fundamental principle of interpretation on tests like this one is that we should never read a question in a way that renders it impossible and thus renders every answer incorrect. For this reason as well, the "or" here must clearly be read as inclusive.

TL;DR: I didn't write this question, but I consider it an excellent question precisely as written, and I wouldn't change a word of it.
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Considering the total number of customers who bought chairs = 2X.
The number of customers who bought tables = 3X.
If half of the customers who bought tables chairs bought were also tables.

The number of customers who bought both tables is included in both the individual ratios. This is equal to X
Hence the number of customers who bought only tables = 3X - X = 2X.
The number of customers who bought only Chairs = 2X - X = X
The customers who bought both tables and chairs = X.
The percentage of customers who bought tables = \(\frac{\left(2X\ +\ X\right)}{4X}\cdot100\ =\ 75\%\)
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*****
The Q Stem says "...customers who bought either tables or chairs"
Therefore Ratio 3:2 does not include those Chair Buyers who have bought tables as well.
Now if 50% Chair Buyers buy Tables as well, then Total Table Buyers = 3x + x = 4x and Total Chair Buyers = 2x
Therefore % of Customers who bought Tables = 4x/6x = 66.66% (Not an option) = approx. 65% (Option B)
Experts may please Comment

Sorry, but this is not true. A customer who bought both chairs and tables is, in fact, a customer who bought "either tables or chairs." It is standard practice to use "or" in an inclusive manner unless otherwise noted, such that "A or B" means "A or B or both."

See my above comments for a lot more discussion on this point.
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Given: Among the customers who bought either tables or chairs at a certain furniture store, the ratio of customers who bought tables to customers who bought chairs is 3:2.

Asked: If half of those who bought chairs also bought tables, what percent of customers bought tables?

Among the customers who bought either tables or chairs at a certain furniture store, the ratio of customers who bought tables to customers who bought chairs is 3:2.

	Bought tables	~Bought tables	Total
Bought chairs			2x
~Bought chairs		0
Total	3x

Half of those who bought chairs also bought tables

	Bought tables	~Bought tables	Total
Bought chairs	x	x	2x
~Bought chairs		0
Total	3x

Filling the rest of the table..

	Bought tables	~Bought tables	Total
Bought chairs	x	x	2x
~Bought chairs	3x-x=2x	0	2x
Total	3x	x	4x

Percentage of customers who bought tables = 3x/4x*100 % = 75%

IMO D
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