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Two Difficult PS problem, Need Help Please!

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by kleef3f » Tue Mar 30, 2010 7:09 pm
1. If n is a positive integer less than 200 and 14n/60 is also an integer, then n has how many different positive prime factors
a.2
b.3
c.5
d.6
e.8
answer:[/spoiler]b
2.The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase
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by thephoenix » Tue Mar 30, 2010 7:19 pm
kleef3f wrote:1. If n is a positive integer less than 200 and 14n/60 is also an integer, then n has how many different positive prime factors
a.2
b.3
c.5
d.6
e.8
answer:[/spoiler]b

14n/60 and n is integer less than 200
implies that n is div by 60
------->n can have any value out of 60,120,180
for all of these prime factors are 2,3,5

total 3
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by ajith » Tue Mar 30, 2010 10:16 pm
kleef3f wrote:1. If n is a positive integer less than 200 and 14n/60 is also an integer, then n has how many different positive prime factors
a.2
b.3
c.5
d.6
e.8
14n/60 is an integer ; 7n/30 is an integer; n is a multiple of 30

n= 30k where k is one of 1,2,3,4,5

whichever the value of k, n will have 2,3,5 as prime factors and n will only have those as prime factors since k<7
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by ajith » Tue Mar 30, 2010 10:19 pm
kleef3f wrote: 2.The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase
Rate of reaction , r = k*A^2/B
Now if B doubles (100% increase)

A^2 should also double to make the rate of reaction unchanged, i.e. A^2 should increase by 100%; A should increase by 41% [Sqrt(2)-1]

Hence D
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