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car and distance

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car and distance

by LevelOne » Fri Jul 03, 2009 7:18 am
How much time did it take a certain car to travel 400 km?

(1) The car traveled the first 200 km in 2.5 hours?
(2) If the car's average speed had been 20 km per hour greater than it was, it would have traveled the 400 km in 1 hour less time than it did.

From (2) I derived:

s+20 = 400/t-1
s = 400/t

am I moving in the right direction? is (2) sufficient because there are two variables and two equations? thanks
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by ssmiles08 » Fri Jul 03, 2009 7:33 am
IMO B.

1) is clearly insufficient. avg speed for 1st half is not necessarily avg speed for second half.

2) (r+20)*(t-1) = 400

we know r*t = 400

rt - r + 20t - 20 = 400

rt - r + 20t = 420

from original equation we can get 400/t = r and substitute it into the above equation.

(400/t)*t - 400/t + 20t = 420

400/t +20t = 20

20t^2 - 20t - 400 = 0

20(t^2 - t - 20) = 0

(t-5)(t+4) = 0

t = 5 or t = -4

time cannot be negative, so it is t = 5. Sufficient. (B)
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by cramya » Fri Jul 03, 2009 7:41 am
am I moving in the right direction? is (2) sufficient because there are two variables and two equations? thanks

I think u got it.

Once we know we can solve we can move on.

Regards,
CR
Last edited by cramya on Fri Jul 03, 2009 7:42 am, edited 1 time in total.
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by LevelOne » Fri Jul 03, 2009 7:41 am
OA is B. ur explanation clears the situation :D
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by m-sand » Mon Apr 19, 2010 1:24 pm
nice
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by Stuart@KaplanGMAT » Mon Apr 19, 2010 3:57 pm
LevelOne wrote: From (2) I derived:

s+20 = 400/t-1
s = 400/t

am I moving in the right direction? is (2) sufficient because there are two variables and two equations? thanks
Great question!

The "# of equations vs # of unknowns" rule is an extremely powerful tool in DS; the better you understand it, the less math you'll have to do to score points (which should make you very happy!).

Here's the full wording of the rule:
To solve a system of n variables, one requires n distinct, linear, equations.
If the question you posted had been an algebra problem, (2) would not have been sufficient, because your equations aren't linear.

A simple definition (certainly sufficient for the GMAT) of a "non-linear" equation is one with an exponent other than one. When we have multiple variables, we often have hard to recognize non-linear equations.

Let's look at your second equation:

s = 400/t.

We can rearrange this to:

st = 400.

This is a non-linear equation since when we isolate t or s in the first equation and then substitute into this one, we'll get an s^2 or t^2 term. When we solve this quadratic, we'll get two solutions, one positive and one negative.

However, it's always important to focus on the content of a particular question; as ssmiles points out, time cannot be negative. In distance/rate/time questions, we can always ignore negative solutions, since they just don't make sense in the real world. Another common area of math in which we can ignore negative solutions is geometry (which is why, for example, when you have r^2 = 36 we don't worry that the radius could be +/-6).

So, since this question is about time, we can ignore the non-linear issue and be confident that our two distinct equations are sufficient to solve for the unknowns.
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