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 number of candidates in 2014 was 500, and there was a 20% increase in the number of candidates per year for the next two years, what is the number of candidates for the LSAT course in 2016? 
 

• A. 90
• B. 95
• C. 100
• D. 108
• E. 115

Hint:

For consecutive percentage increases, you can multiply the initial value by the growth factor \((1 + \text{rate})\) for each period. For example, a 20% increase for two years on a value P is \(P \times (1.2) \times (1.2) = P \times (1.2)\^{}2\). This is faster than calculating the intermediate year's value.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to first calculate the total number of candidates in the year 2016 by applying the year-on-year percentage increase to the base number from 2014. Then, we will use the percentage distribution from the chart for 2016 to find the absolute number of LSAT candidates.
Step 2: Key Formula or Approach:
1. Start with the number of candidates in 2014.
2. Calculate the total candidates in 2015 by applying a 20% increase.
3. Calculate the total candidates in 2016 by applying another 20% increase to the 2015 total.
4. Read the percentage of LSAT candidates in 2016 from the chart.
5. Calculate the number of LSAT candidates by taking that percentage of the total candidates in 2016.
Step 3: Detailed Explanation:
The number of candidates in 2014 is given as 500.
There is a 20% increase per year for the next two years.
Number of candidates in 2015 = \(500 \times (1 + 20/100) = 500 \times 1.2 = 600\).
Number of candidates in 2016 = \(600 \times (1 + 20/100) = 600 \times 1.2 = 720\).
So, the total number of candidates in 2016 was 720.
Now, we look at the chart for the year 2016 to find the percentage of candidates for the LSAT course. The LSAT course is represented by the top segment of the bar. The percentages for 2016 are:
GMAT (bottom) = 40%
GRE = 30%
SAT = 15%
LSAT (top) = 15%
(Check: 40% + 30% + 15% + 15% = 100%).
The percentage of candidates for the LSAT course in 2016 is 15%.
Finally, we calculate the number of LSAT candidates in 2016.
Number of LSAT candidates = \(15% \text{ of } 720\)
\[ = 0.15 \times 720 = \frac{15}{100} \times 720 = \frac{3}{20} \times 720 = 3 \times 36 = 108 \] Step 4: Final Answer:
The number of candidates for the LSAT course in 2016 is 108.