In 2002, 30% of the students at Maxwell state University

Question

In 2002, 30% of the students at Maxwell state University were engineering majors. The number of the engineering majors at the university increased by what percent between 2002 and 2003?

(1) In 2003, 45% of the students at the university were engineering majors.

(2) The number of engineering majors at the university increased by 750 between 2002 and 2003.

GyanOne · Answer

(E) it should be.

% increase in engineering majors from 2002 to 2003 = (number of engineering majors in 2003 - number of engineering majors in 2002)/number of engineering majors in 2002

Using statement 1, unless we know the number of students at the university in 2003, we cannot know the number of engineering majors in 2003. Without knowing that, we cannot calculate the % increase in the number of engineering majors from 2002 to 2003. Insufficient.

Using statement 2, we know the numerator of the fraction we need to calculate. However, we don't know the denominator. Insufficient.

Even by combining the two equations, we still do not have the denominator of the equation (the number of engineering majors in 2002). Still insufficient.

LGOdream · Answer

Why Statement (1) is not sufficient has been kind of hard to understand for me. Here's an approach:

Situation 1:

2002: there are 100 total students (S) and 30 engineering majors (EM) -> 30% EM.
2003: there are 1000 S and 450 EM -> 45% EM.

Increase: 450-30/30 = 420/30 = 1400% increase.

Situation2:

2002: there are 1000 S and 300 EM -> 30%
2003: there are 1000 S and 450 EM -> 45%

Increase: 450-300/300 =150/300 = 50% increase.

Here's a question for GyanOne:

Regarding Statement (1), for it alone to be sufficient wouldn't we need the number of total students for both years?

Regards.

EBITDA · Answer

I combined the two statements by building a two-equation system.

Let X be number of students who are engineering majors, and Y the number of students who are not engineering majors.

In 2002: X / (X + Y) = 3/10
In 2003: (X + 750) / (X + 750 + Y + k) = 45/100

I have added a k to Y in order to account for the possible variation in the number of students who are not engineering majors.

Hence, we have a two-equation system with three unknown variables which can give us more than one solution.

Do you agree with my approach?

Could you please explain other alternative ways of solving this problem?

EBITDA · Answer

GyanOne ,

What do you mean by this?

In 2002, 30% of the students at Maxwell state University

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