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1、The rate of a certain chemical reaction is directly proportaional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

Rate = [A]*[A]/[B]

So  [A]*[A]/[B] =  [x*A]*[x*A]/[2B]

x*x = 2

x = 1.414

So A increases around 40%

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2、Each of the students in a certain class received a single grade of P,F or I. What percent of the students in the class were females?

(1) of those who received a P, 40% were females.
(2) of those who received either an F or I, 80% were males.

category P   F   I
male       A  B   C
female    a   b   c

a/(a+A) =.4
(B+C)/(B+C+b+c) = .8

Do you know the value of (a+b+c)/(A+B+C+a+b+c)?

Hell, NO!

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3、Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the retio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z?

(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division X than for Company Z.
(2) More than half of the full-time employees of Company Z are comployees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

category  X     Y
FT           Fx    Fy
PT           Px    Py

1) Fx/Px < (Fx + Fy)/(Px + Py)
2) Fx/(Fx+Fy) > 0.5; Py/(Px + Py) >0.5

Compare Fx/Px vs. (Fx + Fy)/(Px + Py)

1) sufficient
2) Fx>Fy; Py>Px.  Then Fx/Px = (Fx + Fx) / (Px + Px) > (Fx + Fy) / (Px + Py).  Sufficient.

because (Fx + Fx) / (Px + Px) >(Fx + Fy) / (Px + Px) > (Fx + Fy) / (Px + Py)

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4、If x,y,z are integers greater than 1, what is the value of x+y+z?
(1) xyz = 70
(2) x / yz = 7/ 10

xyz=70=2*5*7, x+y+z = 14

x/yz = 7/10. x = 7, y = 5, z = 2; x=70, y=50, z=2