Lesson: Shrinking and Expanding Gaps

Comment on Shrinking and Expanding Gaps

Awesome Stuff !!!
Is such practice available in SC and CR too?
gmat-admin's picture

Yes it is.
For Critical Reasoning (CR), there are practice questions categorized by question type (e.g., Assumption questions under the Assumption questions video - https://www.gmatprepnow.com/module/gmat-critical-reasoning/video/1139) and there are tons more at the bottom of https://www.gmatprepnow.com/module/gmat-critical-reasoning.

This format is difficult to apply to Sentence Correction (SC) questions. The reason for this is that almost all Sentence Correction questions test more than one concept. In fact, in most cases, they test a wide range of concepts.

So, for example, the given sentence may have an error with subject-verb agreement, and among the answer choices, one may have a verb tense error another a parallelism error, another a dangling modifier error, and so on.

Given the variety of different grammatical concepts that can be addressed in one question, it makes little sense to tackle practice questions until you’ve learned all of the required content.

For this reason, ALL of our linked practice questions are at the bottom of the SC module page: https://www.gmatprepnow.com/module/gmat-sentence-correction

Hello Brent,

Can you advise as to how to approach the below type problems using your shrink rate approach?

Eg: Sally is driving on a road to college at 30 Mph. Her friend Joe is driving on the same road 10 Miles behind her at 60Mph. Will they meet? and If they meet at what Time will they meet.

gmat-admin's picture

I'd be happy to help.

We can solve this question using some number sense.

Sally's speed = 30 mph. In other words, for every hour Sally drives, she travels 30 miles.

Joe's speed = 60 mph. In other words, for every hour Joe drives, he travels 60 miles.

So, in ONE HOUR, Joe travels 30 miles more than Sally does. This means that, EVERY HOUR, the gap between them decreases by 30 miles.

This means that in HALF AN HOUR the gap between them decreases by 15 miles, . . .

. . . and it means that in ONE-THIRD OF AN HOUR the gap between them decreases by 10 miles.

Since they started with a 10-mile gap between them, it will take 1/3 of an hour for the gap to be zero (i.e., they meet)

What if we had to take out the distance when they meet instance of time when they meet.

4/7 *42 = 24 miles
gmat-admin's picture

Yes. To be more specific, when they meet YOLANDA will have walked 24 miles (and MARK will have walked 18 miles )

A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A. 48
B. 72
C. 96
D. 120
E. 192

I understand this is shrinking rate question . How to use delay and early without speed and distance
gmat-admin's picture

There are a couple of nice solutions here: https://gmatclub.com/forum/a-bus-from-city-m-is-traveling-to-city-n-at-a...

Let me know if you'd like me to clarify anything.

Hi Brent,
Can you solve this one taking several different approaches. I get that the total time between cities is 4hrs and that the distance between the buses is one hour when they leave the next day, but after that - I'm lost.
gmat-admin's picture

Hi bertyy,

Sure thing. Here's my solution: https://gmatclub.com/forum/a-bus-from-city-m-is-traveling-to-city-n-at-a...

Cheers,
Brent

Thanks Brent
Great step by step solution. I guess I was trying to solve this thing in one simple equation, but it turns out it is better understood (at least for me) conceptually. Unfortunately, I am not at the math god level. Darn!
gmat-admin's picture

One simple equation would be great, but this is a pretty tricky question (in the 750 range)

Cheers,
Brent

Hi Brent,

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

My question: why can’t you solve it like this?

3x + 5x = 100
8x = 100
x = 12.5

Train X goes 62.5 miles (5 x 12.5) and train Y goes 37.5 miles (3 x 12.5).

Why are the distances switched?

gmat-admin's picture

Hi bertyy,

Can you tell me what value x represents in your solution?

Cheers,
Brent

The speed
gmat-admin's picture

The speed of Train X or Train Y?

Ok, I got it. Complete brain block - it was obvious once I stepped away for a while. Thank you!

Brent,
https://gmatclub.com/forum/train-a-is-traveling-at-40-miles-per-hour-and-train-b-is-traveling-on-213325.html#p1866920

In the link above, I am having hard time registering the solution. Is there any advice from you to look at it from a different perspective.
I did watch the shrinking gap problem and I get it. I believe the head start of 15 miles I throwing me off.

Based on your solution, I read that 15 Miles is the distance to catchup, however the train A is also moving (slower) and making progress. I am thinking the distance is unknown but you have used the gap to cover only as 15 miles? Please advice.

Thanks
S
gmat-admin's picture

Link: https://gmatclub.com/forum/train-a-is-traveling-at-40-miles-per-hour-and...

When it comes to shrinking gap questions, all you need to focus on is the GAP. It doesn't matter that each train is moving at its own speed. All that matters is that the gap SHRINKS at a rate of 20 miles per hour.

In 30 minutes, train A travels 20 miles, and train B travels 30 miles.
Since train B travels 10 MILES FARTHER during those 30 minutes, the GAP between them shrinks by 10 miles during those 30 minutes.

Does that help?

Cheers,
Brent

https://gmatclub.com/forum/ashok-and-brian-are-both-walking-east-along-the-same-path-160840.html
please explain.
gmat-admin's picture

Hi Brent,

the below question is really confusing me out. Please help!

Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z?

81
90
105
125
150
gmat-admin's picture

Hi Brent,

Need your help: https://gmatclub.com/forum/mary-and-kate-are-running-clockwise-around-a-circular-track-with-a-cir-195192.html
gmat-admin's picture

Hi Brent,

Need your help:

https://gmatclub.com/forum/marla-starts-running-around-a-circular-track-at-the-same-129172.html?fl=similar
gmat-admin's picture

Hi Brent,

Not sure where I went wrong with my approach on this problem:

Jerry and Jim run a race of 2000 m. First, Jerry gives Jim a start of 200m and beats him by 30 seconds. Next, Jerry gives Jim a start of 3mins and is beaten by 1000m. Find the time in minutes in which Jerry and Jim can run the race seperately?

I drew up an RTD table

r t d
Jerry a t 2,000
Jim b t-30seconds 1,800

Next race

r t d
Jerry a t 2,000
Jim b t+180seconds 1,000

After deriving the equations from the tables I could not get the answer. Did I set up the table wrong?
gmat-admin's picture

Very tricky question!

GIVEN: Jerry gives Jim a start of 200m and beats him by 30 seconds.

If Jerry beats Jim by 30 seconds, then Jerry's travel time is 30 seconds less than Jim's travel time.

Or we can say Jim's travel time is 30 seconds MORE THAN Jerry's travel time.

So, if t = Jerry's travel time, then t + 30 = Jim's travel time (you have t - 30)

Here's my full solution: https://gmatclub.com/forum/jerry-and-jim-run-a-race-of-2000-m-first-jerr...

Cheers,
Brent

Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

I prefer using an RTD table for these questions but I am not getting the right answer:

R T D
15 t+1 d
10 t d-190

According to your approach, I have filled in the table correctly. But the math doesn't seem to be correct
15t + 15 = d
10t = d - 190
15t + 15 -190 = 10t
15t- 175 = 10t
5t = 175
t = 37

What's going on with my approach?
gmat-admin's picture

The problem lies in your initial entry for train B.

The two trains travel a TOTAL of 190 miles.
So, we can say that (train A's distance) + (train B's distance) = 190

You let d = train A's distance
We get: d + (train B's distance) = 190

So, train B's distance = 190 - d (you have d - 190)

Here's my full solution: https://gmatclub.com/forum/trains-a-and-b-are-190-miles-apart-train-a-le...

Cheers,
Brent

Torkuma Teekay Gbaa's picture

Hi Brent,

Below is a question from OG 2015. I assume the approach used is similar to expanding and shrinking gaps but can you explain why this approach was used and show me another way to approach the question? Thanks

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

(A) 15
(B) 16
(C) 25
(D) 40
(E) 46
gmat-admin's picture

I'm having a hard time turning this into a shrinking gap question.

Here's how I solved it: https://gmatclub.com/forum/in-order-to-complete-a-reading-assignment-on-...

I hope that helps.

Cheers,
Brent

Are these kind of questions very common in GMAT?
gmat-admin's picture

In general, distance/rate/time questions are very common on the GMAT. Among those questions, shrinking/expanding gap questions are a little less popular than the others.

So to summaris ethese kind of questions, Always identify the gap and then calculate the distance or time right?

For Datasufficiency questions, if we have two variables like rate and distance of gap or change of speeds that would suffice right? Im just trying to find a mathemathical approach to DS questions
gmat-admin's picture

In most cases, you can identify the gap and then calculate the distance or time. However, it's also conceivable that you could be given information about the distance and/or time with the goal of calculating the gap.

As for your DS question, it's not possible to make a general rule, since it really depends on how the target question is worded.

Cheers,
Brent

Hi Brent,

I have a question rather silly maybe.
But howcan we distingush between a problem that has multiple travels and shrinking and expanding gap. Is there any strategy for it?
gmat-admin's picture

Hi Anazeer,

For expanding/shrinking gap questions, the two travelers are either traveling towards each other or traveling in opposite directions.

Also, for shrinking gap questions, you'll likely be asked about happens when the two travelers meet (i.e., the gap = 0). For expanding gap questions, you'll likely be asked about happens when the two travelers are a certain distance apart.

Cheers,
Brent

Hi Brent,
The below two questions are similar. but the answers are D and A. Why so? Even for the second one I could sy that in five minutes he is ahead by 2 miles, so in 2.5 minutes he is ahead by one mile. Please explain.

https://gmatclub.com/forum/while-on-a-straight-road-car-x-and-car-y-are-traveling-at-129235.html
https://gmatclub.com/forum/tom-and-samuel-are-riding-motorcycles-down-the-highway-at-constant-239203.html
gmat-admin's picture

Question links:
- https://gmatclub.com/forum/while-on-a-straight-road-car-x-and-car-y-are-...
- https://gmatclub.com/forum/tom-and-samuel-are-riding-motorcycles-down-th...

Very good question, Saahithi!!

Notice that statement 1 is the basically the same in both questions. So, it's not surprising that both are sufficient.

However, the two statement 2's are different.
For the 2nd question, you're making a big assumption with statement 2 (Tom left 5 minutes before Samuel.)
You're assuming that Tom and Samuel left from the SAME starting point.
IF that were the case, then your logic would be perfect.
But what if Tom's starting position was 1,000,000 miles BEHIND Samuel's starting position.
In that case, we see that, in only 5 minutes, Tom was able to close the 1,000,000-mile gap and be 2 miles ahead of Samuel.
This would mean that Tom is traveling over 10,000,000 miles per hour in which case it would take less than 1 second Tom to be 3 miles ahead of Samuel.

Does that help?

Cheers,
Brent

Hi Brent ,

I needed a little help with one question:

https://gmatclub.com/forum/m21-184260.html:

In this que , we know that train leaving B will take 2 hrs from the 2nd statement and we also know that every 15 mins a train starts from A , so regardless of how slow and fast they travel , since they would be on the same path they will meet . It will encounter 8 trains , isnt ?

Thankyou !
gmat-admin's picture

Question link: https://gmatclub.com/forum/m21-184260.html

That's not correct. The speed of the trains leaving station A matters.

Let's consider two different scenarios.

CASE I: The trains leaving station A travel at 80 miles per SECOND.
So, at 8:15 the first train leaves station A and, 1 second later, it arrives at station B.
At 8:30 the next train leaves station A and, 1 second later, it arrives at station B.
At 8:45 the next train leaves station A and, 1 second later, it arrives at station B.
.
.
.
At 11:00 the next train leaves station A and, 1 second later, it arrives at station B.

At 11:05, the train leaves station B. During this train's 2-hour trip, it will pass 8 different trains from station A.

CASE II: The trains leaving station A travel at 4 INCHES per HOUR.
So, at 8:15 the first train leaves station A and, 15 minutes later, it has traveled only 1 INCH.
At 8:30 the next train leaves station A and, 15 minutes later, it has traveled only 1 INCH
At 8:45 the next train leaves station A and, 15 minutes later, it has traveled only 1 INCH
At 9:00 the next train leaves station A and, 15 minutes later, it has traveled only 1 INCH
.
.
.
At 11:00 the next train leaves station A and, 15 minutes later, it has traveled only 1 INCH

So, at 11:05, there are already 12 different trains on the track, and they are only inches away from station B.
So, the train leaving station A will pass those 12 trains PLUS more trains that will continue to depart station B every 15 minutes.

Does that help?

Cheers,
Brent

Hi Brent ,

In the question below, why have you applied the shrink rate when both the trains are in the same direction. Isn’t it similar to the Sabi and Gwyn example ?
I used the logic by equating the difference between the distances travelled by the two trains to be 15. I got a bit confused with your approach, could you please clarify my doubt. Thanks in advance ! :)

https://gmatclub.com/forum/train-a-is-traveling-at-40-miles-per-hour-and-train-b-is-traveling-on-213325.html
gmat-admin's picture

Question link: https://gmatclub.com/forum/train-a-is-traveling-at-40-miles-per-hour-and...

In this question, we start with Train A 15 miles AHEAD of Train B.
Since Train B is traveling faster than Train A, Train B will eventually catch up with Train A.
In other words, the gap will eventually shrink from 15 miles to 0 miles.

So, this characteristic makes this a shrinking gap question.

Does that help?

Cheers,
Brent

Yeah it sure does. I was wondering that once the distance becomes zero, from that point onwards it will no longer be a shrinking rate, right ?
Btw, thanks for the prompt reply ! :))
gmat-admin's picture

That's correct.
In the beginning (while Train B is catching up with Train A) the gap will be shrinking.
After Train B has caught up with Train A, the gap will be expanding from that point on.

For the *expanding gap* example, if the 2 people (Sabi and Gwin) were starting from the same point, but moving in opposite directions, the expansion rate would be 40 + 30 = 70?

Thanks.
gmat-admin's picture

That's correct. If Sami and Gwyn were travelling in OPPOSITE directions, their expansion rate would be 70 mph.

Hi Brent,
I went crazy doing this question (link below) as I misunderstood the points at which Mary and Kate were departing. Is the statement of the question valid as it stands?

https://gmatclub.com/forum/mary-and-kate-are-running-clockwise-around-a-circular-track-with-a-cir-195192.html

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