Data Sufficiency

While on a straight road, car X and car Y are traveling at different constant rates. If car X is now 1 mile ahead of car Y, how many minutes from now will car X be 2 miles ahead of car Y?

(1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
(2) 3 minutes ago car X was 1/2 mile ahead of car Y.

Target question: How many minutes from now will car X be 2 miles ahead of car Y?

Given: Car X is now 1 mile ahead of car Y

Statement 1: Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
Notice that we could easily duplicate this scenario in real life.
Start with Car X 1 mile ahead of car Y (given info)
Have Car X drive at 50 mph and car Y at 40mph.
Use a stopwatch to time how long it takes for Car X to be 2 miles ahead of Y.
As you can see, we have enough information to answer the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3 minutes ago car X was 1/2 mile ahead of car Y.
If car X is presently 1 mile ahead, we can see that car X gains 1/2 mile every 3 minutes.
At that rate, car X will gain another 1 mile in 6 minutes.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Zoser wrote:

Statement 1: Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
Notice that we could easily duplicate this scenario in real life.
Start with Car X 1 mile ahead of car Y (given info)
Have Car X drive at 50 mph and car Y at 40mph.
Use a stopwatch to time how long it takes for Car X to be 2 miles ahead of Y.
As you can see, we have enough information to answer the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Hi,

Can you explain how to solve this algebraically using statement 1 info?

Thanks

You bet!

At time = 0, car X is 1 mile ahead of car Y.
We want to know the time it takes for car X to be 2 miles ahead of car Y
In other words, we want to know the time it takes for the GAP between the two cars to increase by 1 mile.

Here's one approach:
Statement 1: Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
So, in 1 hour, car X travels 50 miles, and car Y travels 40 miles
In other words, in 1 hour, car X travels 10 miles FARTHER than car Y travels
In other words, in 1 hour, the GAP between the cars increases by 10 MILES

From this, we can make many conclusions.
For example, in 2 hours, the GAP between the cars increases by 20 MILES
Likewise, in 3 hours, the GAP between the cars increases by 30 MILES
In 1/2 hour, the GAP between the cars increases by 5 MILES
In 1/5 hours, the GAP between the cars increases by 2 MILES
In 1/10 hours (i.e., 6 minutes), the GAP between the cars increases by 1 MILE

DONE!

Zoser wrote:

You bet!

Great Approach!

I also did the below and it gave me a correct answer:

I equaled Car X distance with Car Y distance by adding 1 to Y`s distance

(50/60)*m = {(40/60)*m}+1..... where m is number of minutes

5m/6 = (2m+3)/3
15m = 12m+18
3m = 18
m = 6

What do you think?

Perfect!!