Problem Solving

To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

salma wrote:To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

We're choosing 2 out of 5 chairs and 2 out of n tables. We know that the total number of possible choices is 150.

So, we have:

5C2 * nC2 = 150

5*4/2 * nC2 = 150

10 * nC2 = 150

nC2 = 15

The easiest thing to do at this point is to backsolve. We know that n is greater than 5 (since 5C2 was only 10), but it shouldn't be that much more - let's try n=6:

6C2 = 6!/2!4! = 6*5/2 = 30/2 = 15.. perfect! Choose (A).

Hi Stuart,

Could you please elaborate further on the concept behind this solution?

Thanks,
Anand

To which concept are you referring - combinations?

stuart,

the question states, tables and chairs that are all different from each other. i thought that with all things distinguishable, we use permutations i.e. n!/(n-r)! and not combinations n!/r!(n-r)!

thank you.

Udai Pathania

pathaniaus wrote:stuart,

the question states, tables and chairs that are all different from each other. i thought that with all things distinguishable, we use permutations i.e. n!/(n-r)! and not combinations n!/r!(n-r)!

thank you.

Udai Pathania

No - we use permutations when we care about the order of selection and combinations when order is irrelevant.

In this question, we don't care about the order in which we select the different pieces of furniture, we just about which pieces we select.

If, for example, we were selecting 4 chairs out of 7 and then arranging those chairs in a straight line, we'd use the permutations formula; if we were just selecting 4 chairs out of 7, we'd use the combinations formula.

On some permutations questions, we also worry about whether the items are distinct. I don't think I've ever seen a GMAT combinations question on which we had to worry about duplicates.

salma wrote:To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

5C2 x TC2 =150
5.4/2 x T ( T-1)/2 =150

T(T-1) =30
T^2 -T -30 =0
(T-6) ( T+5) =0

T =6
Choose A.

Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.

Stuart Kovinsky wrote:

sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.

Ok but shouldn't "2 chairs and 2 tables" come directly before "that"?

*TANGENT ALERT*

No math here, if you're looking for math, move along!

There's no need to put it directly before that (in fact, I challenge you to rewrite the sentence to put that where you want without causing a modification error in the remainder of the sentence) - the verb makes it clear to what "that" refers.

sam117 wrote:

Stuart Kovinsky wrote:

sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.

Ok but shouldn't "2 chairs and 2 tables" come directly before "that"?

Ok thanks