There are two cars. One is 200 miles north of the other. Simultaneousl

Question

There are two cars. One is 200 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 30 miles per hour. How many miles apart are the cars after 3 hours?

A. 225
B. 250
C. 275
D. 300
E. 350

A. 225
 B. 250
 C. 275
 D. 300
 E. 350

Lucky2783 · Accepted Answer

Answer B

EMPOWERgmatRichC · Answer

Hi NYCgirl15,

GMAT question writers often 'hide' established math 'patterns' into questions, so learning to spot those patterns can create some really nice short-cuts for you on Test Day.

Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you can "build" a right triangle around:

The right triangle will have a base of 150 and a height of 200. The hidden pattern here is a 3/4/5 right triangle (the 150 lines up with the '3' and the 200 lines up with the '4'). In this way, you can deduce that each side is '50 times' bigger than it's corresponding side:

3/4/5 becomes
150/200/250

Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Dabhishek · Answer

yes.. made 2 right triangles n then found 2 hypotenus n added it... got 350

should've got 3-4-5 triangle property

EMPOWERgmatRichC · Answer

Hi Dabhishek,

It's common to make mistakes during your training (that's one of the reasons why you train - to define your 'weak spots' and improve), so you shouldn't get too down on yourself. To properly improve though, you really have to be diligent with your review. With each question that you get wrong (especially if you get them wrong because of silly/little mistakes), you should redo the question from scratch. Do all of the work on the pad and repeat all of the steps. There's a 'mechanical' aspect to working through questions that many Test Takers do not account for. You can build your skills, knowledge, Tactics AND mechanics all at the same time, if you choose to.

GMAT assassins aren't born, they're made,
Rich

Archit3110 · Answer

draw figure we get a rectangle figure 
width = 200 and length = 150
diagonal = (200)^2+ (150)^2 ; 62500 = 250 
IMO B

anmol950915 · Answer

The question never talks about the shortest distance. We are left tot guess whether we need the shortest arial distance or road distance.

Bunuel · Answer

If nothing else is mentioned, “distance” always means the straight-line (shortest) distance between the two points. So here we need to calculate their separation using the Pythagorean Theorem: after 3 hours, the northern car has gone 60 miles west, the southern car has gone 90 miles east, so they are 150 miles apart horizontally and 200 miles apart vertically. The straight-line distance is \(\sqrt{150^2 + 200^2} = 250\) miles.

ashKing12 · Answer

isn't the shortest distance = perpendicular distance?

also, hypotenuse is the longest side of a triangle so it can't be the shortest distance?

Bunuel · Answer

Please do not complicate a simple problem or overthink it. We are asked for the distance between two points, the cars. There is no such thing as a perpendicular distance between two points. The shortest distance between two points is always a straight line. The perpendicular distance applies only between a point and a line. In this problem, the distance between the two points happens to be the hypotenuse if we refer to the image posted in one of the posts above. Yes, the hypotenuse is the longest side of a triangle, but if we want to go from one end of the hypotenuse to the other, moving along the hypotenuse is the shortest path compared to going along the two legs.

There are two cars. One is 200 miles north of the other. Simultaneousl

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There are two cars. One is 200 miles north of the other. Simultaneousl

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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My Rewards