West View Driving School currently graduates 175 driver's education

Question

West View Driving School currently graduates 175 driver's education students per year, and Start Drive currently graduates 243 driver's education students per year. The number of students graduating from each driver's education program increases each year at a constant rate. If each of these programs continues to graduate an increased number of students annually at its constant rate, in 2 years both schools will graduate the same number of students.

In the table, identify the rates of increase, in annual graduates, for each program that together meet the graduation forecasts described above. Select only one option in each column.

akash2703 · Answer

I am not sure what is the significance of the other graph (Between no. of referrals and days before follow up).

IMO West View - 61% and Start drive - 39%

What we can do is calculate the following parameters for west view and start drive based on the given rate of increase (constant for each year):-

1) Number of students graduating after two years from West View for all the given rates -
26% - 277.83 (175*1.26*1.26 = 277.83)
39% - 338.1175
42% - 352.87
  61% - 453.6175  
73% - 523.7575
84% - 592.48

2) Number of students graduating after two years from Start Drive for all the given rates

26% - 385.7868 (243*1.26*1.26 = 385.79)
  39% - 469.5003  
42% - 489.9852
61% - 629.8803
73% - 727.2747
84% - 822.7008

Which two figures are equal for both the driving schools? Above two highlighted fields.

Hence with the rate of 61% for west view and 39% for Start drive, both schools will graduate the same number of students.

ktzsikka · Answer

Start Drive=39%
West View=61%

Sajjad1994 · Answer

OA of this question is:

West View : 73
 Start Drive : 39

I will post the OE.

This comes to the end of the competition, Thank you to everyone who participated in this event. I will announce the winners tomorrow.

Thank you

Sajjad1994 · Answer

Official Explanation

The correct answers are 73 graduates per year for West View Driving School and 39 graduates per year for Start Drive.

Let x = increase in the number of graduates at West View, and y = increase in the number of graduates at Start Drive. Then, according to the given information,
 175+2x=243+2y , which is equivalent to  34=x-y . The only pair of numbers in the table that satisfies this equation are 73 and 39. If West View increases its number of graduates by 73 students per year, in 2 years it will graduate 321 students per year. If Start Drive increases its number of graduates by 39 students per year, in 2 years it will graduate 321 students per year as well.

ktzsikka · Answer

As per my understanding - question indicates number of students increasing at a  'constant rate' . Hence the equation should be  75(1+\frac{x}{100})^2  instead of  75+2x .
Please advise on how to differentiate between these two scenarios?

Sajjad1994 · Answer

Wow! An easy question made very hard by some unnecessary equation.

First of all, understand what question is demanding

West View Driving School currently graduates 175 driver's education students per year, and Start Drive currently graduates 243 driver's education students per year. The number of students graduating from each driver's education program increases each year at a constant rate. If each of these programs continues to graduate an increased number of students annually at its constant rate, in 2 years both schools will graduate the same number of students.

In the table,  identify the rates of increase, in annual graduates , for each program that together meet the graduation forecasts described above. Select only one option in each column.

We have to simply identify at what specific rate of each school (in terms of the number of gradutes), after two-year, the number of school graduates will be equal.

Method 1 by using algebra equation.

175+2x=243+2y

175 in the above equation is the current number of graduates of West View Driving School
2 in the above equation is used for the 2 years
x is the number of graduates per year which we have to find so that the equation be equal

243 in the above equation is the current number of graduates of Start Drive School
2 in the above equation is used for the 2 years
y is the number of graduates per year which we have to find so that the equation be equal

Solving the equation we can find that

x-y=34

It means the school currently has a less number of graduates need 34 more students for each of the two years to be equal to the other school. 
The next step is to select values that satisfy this condition.

Only answers 73 and 39 satisfy the condition.

Let's verify it

West View Driving School current graduated: 175
After one yaer = 175+73 = 248
After two yaers = 248=73 = 321

Now the other school having more graduates currently

Start Drive school current graduates: 243
After one year = 243+39 = 282
After two yaers = 282+39 =321

So that's the answer

West View: 73
Start Drive: 39

Method 2 is by testing the options provided and coming to the answer which satisfies the requirement but it may go beyond 2 minutes and 30 seconds so we are not going to discuss that.

Coming to your submitted answer

Start Drive=39%
West View=61%

There is no need for the answer in percentage as the question clearly stated that  identify the rates of increase, in annual graduates

61+61+175 = 297
39+39+243 = 321

Both sides are not equal.

ivycation2024 · Answer

This is such a bad question, it will never show up in the real OG test. Rate* but in the unit of "graduates/year" ?

West View Driving School currently graduates 175 driver's education

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West View	Start Drive	Rate of increase (graduates per year)
		26
		39
		42
		61
		73
		84