Philip has m shirts and n trousers in his wardrobe, where the number

Question

Philip has m shirts and n trousers in his wardrobe, where the number of shirts is at least two times the number of trousers. The total ways Philip could select a combination of shirt and trouser is 36.

Select for  Maximum n , the maximum possible value of n and select for  Minimum n , the minimum possible value of n, that are consistent with the given information above. Make only two selections, one for each column.

chetan2u · Accepted Answer

Philip has m shirts and n trousers in his wardrobe, where the number of shirts is at least two times the number of trousers.  
We are given  m\geq 2n .

The total ways Philip could select a combination of shirt and trouser is 36. 
Shirt can be chosen in m ways and the trouser in n ways, so total possible combinations = m*n = 36

Let us factorize 36 to get possible combiations = 36*1 = 18*2 = 12*3 = 9*4 = 6*6. 
 As m is at least two times n, both values cannot be same, so discad 6*6. 
The remaining values can fit in => m*n =   36*1 = 18*2 = 12*3 = 9*4

Maximum n:  We know m*n is 36 and the possible combinations give 9*4 as an option that has the maximum value of n.  Hence, maximum n = 4 
 Minimum n:  We know m*n is 36 and the possible combinations give 36*1 as an option that gives the minimum value of n.  Hence, minimum n = 1

thisischelso · Answer

We need to find combinations of shirts and trousers.

We know that M is greater than or equal to 2N

and M X N should be 36

So M, N could be

36, 1 
18, 2
12, 3
9, 4 
6, 6 ----> note that this doesn't meet the condition that M is equal to or OR GREATER than 2N.

So min N is 1. Max N is 4

Gemmie · Answer

m: number of shirts n: number of trousers m >= 2n m * n = 36 => 2 * n^2 <= 36 => n^2 <= 18 => n^2 could be 16, 9, 4 or 1 => n could be 4, 3, 2 or 1 min n: 1 max n: 4

jessjitsingh · Answer

I don't think the answer to this question is correct.

The maximum as 4 makes sense but technically, the minimum value of n can be 0. The question stem says that the the number of shirts is at least two times the number of pants and the way Philip can choose a combination of a shirt and a trouser is 36 which means:
1. M>=2N
2. MC1*NC1 = 36
Now, if I take N as 0 and M as 36, technically, both those conditions are satisfied (yes, 0C1 is equal to 1 -> Philip can choose 0 trousers in 1 way i.e. by not choosing a trouser) so I am not sure why 1 is the minimum value. Can someone/ admin please explain?

nguyenpham1309 · Answer

I think the constrain of what you are saying is this sentence: "The total ways Philip could select a combination of shirt and trouser is 36."
I believe that every sentence has its meaning in the way of support us to eliminate the options. At first, I wonder why they have to specifically mention the "combination". If I can demonstrate this sentence in terms of math, it should be m*n = 36. When I see the minimum n can be zero, I think "Is n=0 violate the combination of m*n = 36?", or "If n = 0 means Philip cannot choose a trouser, does this action still satisfy the requirement of choose a combination of a shirt and a trouser?"

And to be honest, I think GMAT encourages us to think practically, not math technically. This question is not the only one to prove that idea.

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Philip has m shirts and n trousers in his wardrobe, where the number

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