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integrated reasoning question

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Junior | Next Rank: 30 Posts
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by lj88 » Fri Mar 15, 2013 6:49 pm
Between 2008 and 2012, the number of computer science teachers decreased despite a jump in computer science majors from 400 in 2008.
In the given expressions, T and S represent the percent change in the number of teachers and computer science students, respectively, over the four years and R represents the the number of computer science students per teacher in 2008.

Percent change in a quantity X is calculated using the formula
(X recent − X old) / (X old) * 100.

Select the expression that represents the number of teachers in 2012 and select the expression that represents the number of computer science students per teacher in 2012.

Choices:
A) (400/R)([100-T]/100)
B) R([100+S]/[100+T])
C) 1/R
D) R([100-T]/[100+S])
E) (400/R)([100+T]/100)

OA: # of teachers in 2012 [spoiler](E)[/spoiler] / # of CS students per teachers in 2012 [spoiler](B)[/spoiler]

Thank you!
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by Anju@Gurome » Fri Mar 15, 2013 8:10 pm
lj88 wrote:Between 2008 and 2012, the number of computer science teachers decreased despite a jump in computer science majors from 400 in 2008.
In the given expressions, T and S represent the percent change in the number of teachers and computer science students, respectively, over the four years and R represents the the number of computer science students per teacher in 2008.

Percent change in a quantity X is calculated using the formula
(X recent − X old) / (X old) * 100.

Select the expression that represents the number of teachers in 2012 and select the expression that represents the number of computer science students per teacher in 2012.
Number of students in 2008 = 400
Number of teachers in 2008 = 400/R

Number of students in 2012 = 400 + S% of 400 = 400 + (S/100)*400 = (400 + 4S) = 4(100 + S)
Number of teachers in 2012 = 400/R + T% of 400/R = 400/R + (T/100)*(400/R) = (400/R)(1 + T/100) = (400/R)[(100 + T)/100] ----> Option E = 4(100 + T)/R

Number of students per teacher in 2012 = (number of students)/(number of teachers) = 4(100 + S)/[4(100 + T)/R] = R(100 + S)/(100 + T) ----> Option B
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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