Question: An art gallery owner is hanging paintings for a new show. Of the six paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?

1. 18
2. 30
3. 64
4. 120
5. 216

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. This one comes particularly from permutation and combination.

The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

Given in the question, the proprietor of an art gallery is now hanging paintings in preparation for a new exhibition. Only three of the six paintings that she has chosen from will fit on the main wall of the gallery, so she will have to choose carefully. If we assume that she will hang as many of them as she can on that wall, how many different ways are there for her to arrange the paintings?

We have got six paintings out of which we have to permute 3 paintings.
This can be done in 6P3 ways.
6! / 3! = 120 ways.

D is the correct answer.

Approach Solution 2:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. This one comes particularly from permutation and combination.

The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

given in the question that the proprietor of an art gallery is now hanging paintings in preparation for a new exhibition. Only three of the six paintings that she has chosen will fit on the main wall of the gallery, so she will have to choose carefully. If we assume that she will hang as many of them as she can on that wall, how many different ways are there for her to arrange the paintings?

The first painting can be chosen in 6 ways.
The second painting can be chosen in 5 ways.
The third painting can be chosen in 4 ways.
Now we can use fundamental principle of counting we can get the final answer.
The total number of ways to choose the 3 paintings will be 6*5*4 = 120

D is the correct answer.

Approach Solution 3:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. This one comes particularly from permutation and combination.

The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

Given in the question that the proprietor of an art gallery is now hanging paintings in preparation for a new exhibition. Only three of the six paintings that she has chosen from will fit on the main wall of the gallery, so she will have to choose carefully. If we assume that she will hang as many of them as she can on that wall, how many different ways are there for her to arrange the paintings?

We have got six paintings out of which we have to permute 3 paintings.
The paintings can be chosen in 6C3 ways.
6! / (6-3)! 3! = 20 ways.

Now, in these 20 ways, three paintings are selected.
Now they can be arranged in 3! Ways
The final answer will be 20 * 3! = 120 ways

D is the correct answer.

“An art gallery owner is hanging paintings for a new show. Of the six" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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