Question: A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same color is?

1. 12x81
2. 16 x 192
3. 20x 125
4. 24x216
5. None of the above

Correct Answer: (A)
Solution and Explanation:
Approach Solution 1:

The problem statement states that

Given:

• A new flag is to be designed with six vertical stripes.
• It is designed using some or all of the yellow, green, blue or red colors.

Find out:

• The number of ways this can be done so that no two adjacent stripes have the same color.

Total number stripes= 6 stripes

We can design each stripe with any of the 4 colours.
I I I I I I
Therefore, the first can be any of the four
4 I I I I I
The next subsequently can be any of the 4 but the one used in the first stripe, so 3
4*3 I I I I
Likewise, the next can be any but the one used in 2nd stripe
4*3*3 I I I

Therefore, the number of ways this can be done so that no two adjacent stripes have the same color = 4*3*3*3*3*3=12*81

Approach Solution 2:

The problem statement informs that

Given:

• A new flag is to be designed with six vertical stripes.
• It is designed using some or all of the yellow, green, blue or red colors.

Find out:

• The number of ways this can be done so that no two adjacent stripes have the same color.

There are 6 verticle stripes and 4 colors to design them.
In the case of the first stripe, we can use all 4 colors - no constraints.
In the case of the second stripe, however, we cannot select the color already picked for the first one, hence 4-1 = 3.
In the case of the third stripe, we cannot select the color, picked for the second, but can select one used for the first - again 3. Identical logic for the remaining stripes.

Therefore, the final result: 4∗3∗3∗3∗3∗3= 4∗ 3^5 = 12∗81

Approach Solution 3:

The problem statement discloses that

Given:

• A new flag is to be designed with six vertical stripes.
• It is designed using some or all of the yellow, green, blue or red colors.

Find out:

• The number of ways this can be done so that no two adjacent stripes have the same color.

Let's say that the flag is prepared only by any two of the four colors all held at the alternate positions Then no of cases= 2*4C2
In a similar way, for 3 of the 4 cases taken
4C3 * 3 * 2^5.

Therefore, for all four cases taken= 12*81

“A new flag is to be designed with six vertical stripes using some''- asks the candidates to use their capabilities to crack the problem. It is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions aim to measure candidates’ analytical knowledge to solve quantitative problems. GMAT Quant practice papers help the candidates to go through various questions that will improve their quantitative skills.

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