Problem Solving

1.If b = 9 and , then all of the following are not possible values of x EXCEPT

a.-3
b.-2
c.0
d.2
e.3

2.Andrew is driving at a constant rate of speed to visit his friend Jason who lives 440 miles away. If Andrew were to increase his speed by 4 miles per hour, then his driving time would decrease by one hour. What is Andrew’s current rate of speed in miles per hour?
4
10
11
40
44

Thank u !!!!

You've left smth out of problem 1. It cannot be solved as it is because we do not know anything about x.

Say s = Andrew's speed and t = time it takes to get to his friend.
You have that s*t = 440. We notice that t = 440/s
In addition, (s + 4)(t - 1) = 440. This means that st - s + 4t - 4 = 440. Since st = 440, then we get that 4t - s - 4 = 0. Now we substitute t with 440/s, which means that 1760/s - s - 4 = 0. Now let's multiply this equation with s and we get that 1760 - s^2 - 4s = 0. This is equivalent to

s^2 + 4s - 1760 = 0. Now, since 1760 = 4*440, then we can safely assume that 1760 = 40 * 44. So our equation will be (s - 40)(s + 44) = 0. Since 40 is the only positive solution to this equation (speed cannot be negative!), then you get s = 40. Answer D.

A quick look at answer choices gave me a hint

since D=S*T and T=D/S

Try out choice D. We have D given as 440 so T= 440/40 = 11

If S increased by 4 so T should decrease by 1. Let's try to 40+4

T= 440/44 = 10

T decreased by 1, hence 40 is the correct choice

rolrol19 wrote:A quick look at answer choices gave me a hint

since D=S*T and T=D/S

Try out choice D. We have D given as 440 so T= 440/40 = 11

If S increased by 4 so T should decrease by 1. Let's try to 40+4

T= 440/44 = 10

T decreased by 1, hence 40 is the correct choice

That's a really nice approach rolrol, thanks.

rolrol19 wrote:A quick look at answer choices gave me a hint

since D=S*T and T=D/S

Try out choice D. We have D given as 440 so T= 440/40 = 11

If S increased by 4 so T should decrease by 1. Let's try to 40+4

T= 440/44 = 10

T decreased by 1, hence 40 is the correct choice

Dana knows her math!!!, but this is the fast way. saves time on the GMAT...

Thank you very much.

Can i get help with this to?

If b = 9 and x^2-b/x^2-4=9/4 , then all of the following are not possible values of x EXCEPT

a.-3
b.-2
c.0
d.2
e.3

IMO C

(x^2 -9)/(x^2-4) = 9/4

backsolving can help here, for values -3,-2,2 or 3 the right hand side of the equation does not equate to the left hand side.