Question: A pie is divided into 3 equal parts. The first part is divided equally between 2 people, the second part is divided equally among 4 people, and the third part is divided equally among 5 people. What percentage is the ratio between the smallest servings of the pie, to the largest serving of the pie (to the nearest integer)?

1. 39%
2. 40%
3. 41%
4. 42%
5. 43%

Solution and Explanation:

Approach Solution (1):
Let the total length the pipe = 300
It is divided into 3 parts, so each parts measures = 100
1st part is divided among 2 people. Length of each part = 50, 50
2nd part is divided among 4 people. Length of each part = 25, 25, 25, 25
3rd part is divided among 5 people. Length of each part = 20, 20, 20, 20, 20
Smallest length : Highest length = 20 : 50 = 40%

Correct option: B

Approach Solution (2):
Let’s find the size of each of the 3 equal parts. Because each can be divided equally by 2, 4, and 5 and we want to work with integers, let’s find the least common multiple of 2, 4, and 5, which is 20.
It means that the first part was divided in 2 pieces of 10 each (largest), and the last part was divided in 5 pieces of 4 each (smallest)
Ratio of the smallest to largest =\({4\over10}\)= 0.4 = 40%

Correct option: B

Approach Solution (3):
Picking numbers
Pick the whole pie is 300
Part I = Part II = Part III = 100
Part I: divided equally 2 --- 50 each
Part II: divided equally 4 --- 25 each
Part III divided equally 5 --- 20 each
Ratio\(\frac{Smallest}{Largest}=\frac{20}{50}*100 \)=40%

Correct option: B

“A pie is divided into 3 equal parts. The first part is divided equally between 2 people, the second part is divided equally among 4 people, and the third part is divided equally among 5 people. What percentage is the ratio between the smallest servings of the pie, to the largest serving of the pie (to the nearest integer)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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