Some of the students enrolled at college T are part-time

There is no information about increase/decrease of part time students in either statement so my pick is E , let me know what is OA.

if you pick numbers lets say in 99

FullTime=700
partTime=300

in 2000

FullTime=750
partTime=300 (stays the same since 5% increase is all counted in Full Time students )

scenario 2

in 99
FullTime =1300
PartTime=700
in 2000
FullTime=1350
Partime=750

% increase of fulltime students gives different answer for both the scenarios and hence my answer is E

Some of the students enrolled at college T are part-time students and the rest are full-time. By what percent did the number of full-time students enrolled at college T increase from fall of 1999 to the fall of 2000?

1) There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.
2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.

Image:

Answer should be E, and if you want to find the% increase of some thing then in that case we need to have to 2 data available.
1. Change( which is thr in 1 part)
2. original value or the value of fall 1999

so only one information is available so answer is E.

hope it helps

CASE 1:

	Total Students	Full-time students	Part-time Students
Fall 1999	100	10	90
Fall 2000	105	60	45
% Change	5% increase	50 more students, a 500% increase	Not Required

CASE 2:

	Total Students	Full-time students	Part-time Students
Fall 1999	100	25	75
Fall 2000	105	75	30
% Change	5% increase	50 more students, a 200% increase	Not Required

Not Sufficient.

Ans: "E"

(1)

insufficient

(2)
no differentiation between part-time and full-time students
insufficient

(together)
we still don't know anything about the # of part-time students, which is an essential contributor to the 5% increase mentioned in statement (2)
examples:
- if there are 0 part-time students in both years, then the # of full-time students has increased by 5%
- if the # of full-time students has increased from 0 to 50 but the # of part-time students has remained constant at 1000 (so that 50 is 5 percent of the enrollment), then the # of full-time students has grown by infinity%
...and anything in between

answer = E

VeritasPrepKarishma, Bunuel, chetan2u
I did understood the solution and agree that answer should be E, but I also fall into trap of choosing B in the first go.
Could you please explain how to answer this question algebraically without taking numbers?
I am just not able to understand whats wrong with the approach of taking initial values to be X+Y and final values 1.05(X+Y)!

Hello Moderators,
any update on this one?

(1)
no indication of the size of the student body
insufficient

(2)
no differentiation between part-time and full-time students
insufficient

(together)
we still don't know anything about the # of part-time students, which is an essential contributor to the 5% increase mentioned in statement (2)
examples:
- if there are 0 part-time students in both years, then the # of full-time students has increased by 5%
- if the # of full-time students has increased from 0 to 50 but the # of part-time students has remained constant at 1000 (so that 50 is 5 percent of the enrollment), then the # of full-time students has grown by infinity%
...and anything in between

answer = e

Sn: the new number of full time students.
So : the old number of full time students

The question is asking for Z as
Z = ( Sn - So) / So

1) There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.

=> Sn - So = 50
We dont know So value so we cannot calculate Z.
Insuff.

2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.

=> We have no clue whether an increase in the number of total student corellates with a rise in the number of full time students or not.
Insuff.
So E is the answer.

Posted from my mobile device

bumping gmatbusters niks18 amanvermagmat Bunuel VeritasPrepKarishma
for validating the approach/ suggesting an efficient one.

Step 1: simplify the questions stem to simplest form, I used algebraic approach to form linear equations.

Step 2: write algebraic form of equations for both the statements. As seen here, the main question asks for ratio of
difference of absolute values in numerator to the absolute value in denominator.
St 1 gives the difference, but the absolute value of denominator is not known.
St 2 seems to be providing no info in the context of what the question is asking.

Combining the statements, I still do not see arriving at an unique value for denominator, Hence (E)

1) There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.
Since we do not know the number of full time students, this 50 can be very small or very large.
-if in 1999, there was only 1 full time student, and in 2000 number increased by 50, then no. of students = 51
% increase = \(\frac{50}{1}\)*100 = 5000%
-if in 1999, there were 1000 full time student, and in 2000 number increased by 50, then no. of students = 1050
% increase = \(\frac{50}{1000}\)*100 = 5%
Hence insufficient.

(PS: you need not do the above calculation. Remember since we do not know the base value, increase in value will never be sufficient to find the percentage increase.)

2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.
It is similar to St 1: since we don't know the initial total number of students, we can not find the number of total number/full time students.
hence insufficient.

Even after combining St 1 & 2, we are unable to find the number of full time students which is required to find the % increase in full time students. Hence NOT SUFFICIENT.

Check your understanding :
if we change the second statement as:

New Statement2):The number of full time students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.
Now find the number of Part time time students in 2000.

Hi adkikani

Your equation for second statement is flawed, you forgot to put a bracket required to provide the effect of factor of 1.05.
See sketch.
now , even if you get correct equations, if you are not able to conclude further, it is not of much use.
In my opinion, this is not the best approach.

Nice catch gmatbusters


I have edited the steps in my original post to clear the fog.

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