Seeking advice for picking Smart Numbers

[jasonthomasyee]

I hope it's alright that I post the entirety of this Manhattan CAT question:

It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?

Answer: (z(y-x))/(x+y)

The explanation suggests picking x=2 (ie 15 mph), y=3 (ie 10 mph), and z=30.

After the first hour both trains have traveled a combined 25 miles, leaving a distance of 5 miles between them. Since out of these initial 25 miles X traveled 3/5 of the distance (15 miles) and X traveled 2/5 of the distance (10 miles) we expect that ratio to hold true for the remaining 5 miles. Therefore out of the 30 miles between them to start, X traveled 18 miles and y traveled 12 miles.

However, I chose numbers X=3 (20 mph), Y=4 (15 mph), Z=60. After one hour, X travels 20 miles and Y travels 15 miles for a combined 35 miles. In this case, X travels 4/7 of the 35 miles and Y travels 3/7 of the 35 miles. However, I hit a wall because I don't know what to do with the 25 remaining miles since 25 is not divisible by 7 so I can't set up a clean ratio.

My question is... How do I mitigate running into this wall? I made sure to choose small numbers for X and Y as Stacey recommends... is there another strategy I should keep in mind as well?

Thanks,

Jason

[jasonthomasyee]

I hope it's alright that I post the entirety of this Manhattan CAT question:

It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?

Answer: (z(y-x))/(x+y)

The explanation suggests picking x=2 (ie 15 mph), y=3 (ie 10 mph), and z=30.

After the first hour both trains have traveled a combined 25 miles, leaving a distance of 5 miles between them. Since out of these initial 25 miles X traveled 3/5 of the distance (15 miles) and X traveled 2/5 of the distance (10 miles) we expect that ratio to hold true for the remaining 5 miles. Therefore out of the 30 miles between them to start, X traveled 18 miles and y traveled 12 miles.

However, I chose numbers X=3 (20 mph), Y=4 (15 mph), Z=60. After one hour, X travels 20 miles and Y travels 15 miles for a combined 35 miles. In this case, X travels 4/7 of the 35 miles and Y travels 3/7 of the 35 miles. However, I hit a wall because I don't know what to do with the 25 remaining miles since 25 is not divisible by 7 so I can't set up a clean ratio.

My question is... How do I mitigate running into this wall? I made sure to choose small numbers for X and Y as Stacey recommends... is there another strategy I should keep in mind as well?

Thanks,

Jason

Just want to bump this thanks to the spammers

[RonPurewal]

Hi,
Please re-post this question in the correct folder (either MGMAT CAT Math or MGMAT non-CAT Math, depending on the source of the question).

Yes, it's OK to post the question in its entirety. In fact, per the forum rules, you must post the question in its entirety.

Thanks.