Question:
The following chart shows the percent distribution of the number of candidates enrolled in a certain test-prep company from 2014 to 2017 for four courses: GMAT, GRE, SAT and LSAT.
If the total number of candidates increased by 40% from the year 2014 to the year 2017, what is the simple annual percent increase (if necessary the whole number rounded) in the number of candidates for the GMAT course between 2014 and 2017?
The following chart shows the percent distribution of the number of candidates enrolled in a certain test-prep company from 2014 to 2017 for four courses: GMAT, GRE, SAT and LSAT.
If the total number of candidates increased by 40% from the year 2014 to the year 2017, what is the simple annual percent increase (if necessary the whole number rounded) in the number of candidates for the GMAT course between 2014 and 2017?
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In problems involving percentages of an unknown total, it's often easiest to assume the initial total is 100. This simplifies calculations as percentages directly translate to absolute numbers. Remember that simple annual increase is the total increase divided by the number of years, not a compounded calculation.
Updated On: Oct 3, 2025
- 20%
- 25%
- 27%
- 30%
- 33%
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
This problem requires us to calculate the change in the absolute number of GMAT candidates and then find the simple annual percentage increase over a 3-year period. Since we are not given the absolute number of total candidates, we can assume a variable to represent it.
Step 2: Key Formula or Approach:
1. Assume the total number of candidates in 2014 is \(T\).
2. Calculate the total number of candidates in 2017 based on the 40% increase.
3. Read the percentage of GMAT candidates for 2014 and 2017 from the chart.
4. Calculate the absolute number of GMAT candidates for both years in terms of \(T\).
5. Calculate the total percentage increase for GMAT candidates from 2014 to 2017.
6. Calculate the simple annual percent increase by dividing the total percentage increase by the number of years (3).
Step 3: Detailed Explanation:
Let's assume the total number of candidates in 2014 was \(T = 100\).
The total number of candidates increased by 40% from 2014 to 2017.
Total candidates in 2017 = \(100 \times (1 + 0.40) = 140\).
From the chart, we read the percentage of candidates for the GMAT course:
Percentage of GMAT candidates in 2014 = 35%.
Percentage of GMAT candidates in 2017 = 45%.
Now, let's calculate the number of GMAT candidates in each year:
Number of GMAT candidates in 2014 = \(35\% \text{ of } 100 = 0.35 \times 100 = 35\).
Number of GMAT candidates in 2017 = \(45\% \text{ of } 140 = 0.45 \times 140 = 63\).
Next, we find the total percentage increase in the number of GMAT candidates from 2014 to 2017.
Total % Increase = \(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\)
Total % Increase = \(\frac{63 - 35}{35} \times 100 = \frac{28}{35} \times 100 = \frac{4}{5} \times 100 = 80\%\)
The period is from 2014 to 2017, which is a span of 3 years (2014-2015, 2015-2016, 2016-2017).
The simple annual percent increase is the total percent increase divided by the number of years.
Simple Annual % Increase = \(\frac{80\%}{3} \approx 26.67\%\)
Rounding to the nearest whole number, we get 27%.
Step 4: Final Answer:
The simple annual percent increase in the number of candidates for the GMAT course is 27%.
This problem requires us to calculate the change in the absolute number of GMAT candidates and then find the simple annual percentage increase over a 3-year period. Since we are not given the absolute number of total candidates, we can assume a variable to represent it.
Step 2: Key Formula or Approach:
1. Assume the total number of candidates in 2014 is \(T\).
2. Calculate the total number of candidates in 2017 based on the 40% increase.
3. Read the percentage of GMAT candidates for 2014 and 2017 from the chart.
4. Calculate the absolute number of GMAT candidates for both years in terms of \(T\).
5. Calculate the total percentage increase for GMAT candidates from 2014 to 2017.
6. Calculate the simple annual percent increase by dividing the total percentage increase by the number of years (3).
Step 3: Detailed Explanation:
Let's assume the total number of candidates in 2014 was \(T = 100\).
The total number of candidates increased by 40% from 2014 to 2017.
Total candidates in 2017 = \(100 \times (1 + 0.40) = 140\).
From the chart, we read the percentage of candidates for the GMAT course:
Percentage of GMAT candidates in 2014 = 35%.
Percentage of GMAT candidates in 2017 = 45%.
Now, let's calculate the number of GMAT candidates in each year:
Number of GMAT candidates in 2014 = \(35\% \text{ of } 100 = 0.35 \times 100 = 35\).
Number of GMAT candidates in 2017 = \(45\% \text{ of } 140 = 0.45 \times 140 = 63\).
Next, we find the total percentage increase in the number of GMAT candidates from 2014 to 2017.
Total % Increase = \(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\)
Total % Increase = \(\frac{63 - 35}{35} \times 100 = \frac{28}{35} \times 100 = \frac{4}{5} \times 100 = 80\%\)
The period is from 2014 to 2017, which is a span of 3 years (2014-2015, 2015-2016, 2016-2017).
The simple annual percent increase is the total percent increase divided by the number of years.
Simple Annual % Increase = \(\frac{80\%}{3} \approx 26.67\%\)
Rounding to the nearest whole number, we get 27%.
Step 4: Final Answer:
The simple annual percent increase in the number of candidates for the GMAT course is 27%.
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