Data Sufficiency

Viper83 wrote:Is this setup correct?
1. is obviously insufficient because we dont know anything about the additional 200 km.
2. we have 400=rt from the prompt. From statement 2 we get 400=(r+20)(t-1). Now we have 2 equations and can solve for t. Is this correct?

Yes, it's correct but careless.
There is more to solving the equations than just saying "we have two equations in two unknown, hence we can solve..". That statement only holds strong when the equations are linear and independent of each other.

In this case, rt = 400 ........ (1)
And, (r + 20)(t - 1) = 400 .... (2)

Now replacing 400 in (2) by rt from (1), we have

• --> (r + 20)(t - 1) = rt
  --> (rt + 20t - r - 20) = rt
  --> (20t - r - 20) = 0 ......... (3)

Now, replacing r = 400/t from (1) in (3),

• --> (20t - 400/r - 20) = 0
  --> (20t² - 20t - 400) = 0
  --> (t² - t - 20) = 0 .......... (4)

Solving (4) we get, t = 5 or t = -4

Now in this case t = -4 is not possible, hence t = 5.
BUT what if the equation gave two possible solution for t? In that case statement 2 wouldn't had been sufficient.

Viper83 wrote:Thanks Anurag, so in this kind of question one should actually solve to get the answer since it is a quadratic equation?

In my opinion, yes.

anuragvaid wrote:Anurag,

Its my mistake.....U had indeed correctly mentioned the solution to be 5...dunno, Y I read 4....

No no. Not yours.
You're correct. I edited that after seeing your post. I thought I had posted a message acknowledging that!