GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Dec 2018, 04:25

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar

Train A leaves New York for Boston at 3 PM and travels at

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7106
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 13 May 2016, 21:28
anandmehrotra wrote:
I assumed that train B travelled 100 miles in 10 minutes(started at 3:50 and met Train A at 4:00 pm), as that is when both trains met. Since B travelled 100 miles in 1/6 of an hour, it must be going at 600 mph. Am I making an incorrect assumption here?



Let the distance be D..
the two meet each other after A has travelled for 1 hour that is 100*1 = 100miles...
now it meets the other train coming from other side..
the other train has travelled for 10 min as you have correctly stated but it does not travel 100 miles..
IT travels D-100 miles.. and Now you have to work further
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 22 Sep 2012
Posts: 2
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 23 Sep 2016, 09:41
Let the distance travelled by Train B when both the trains meet at 4 pm be x miles.
Therefore, speed of train B = x miles / 10 minutes
= 6x miles per hour

At 4 pm, Train A has travelled for 60 minutes, and Train B has travelled for 10 minutes.
Thus total time travelled = 70 minutes.
Remaining total time for both trains to cover their respective distance = 2hours - 70 minutes
= 50 minutes
= \frac{5}{6} hours

Now, train A has travelled 100 miles in 1 hour, and train B has travelled x miles so far.
Total distance between New York and Boston = (100 + x) miles
Remaining distance to be covered by train A = x miles, and remaining distance to be covered by train B = 100 miles.

Time taken to do so, by train A = \frac{x}{100} hours
Time taken to do so, by train B = \frac{100}{6x} hours

By definition, \frac{x}{100} + \frac{100}{6x} = \frac{5}{6}
Solving, we get \(6x^2 -500x + 10000 = 0\)

x = \frac{100}{3} or 50

Then, as other users have mentioned, each statement can be shown to be sufficient to answer the question.
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 510
Location: India
Premium Member
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 23 Feb 2017, 04:56
Prompt analysis
Let the distance be x, speed of train B be v, t be the time taken after departure to meet train B
x = v/6 +100*1
x/v +x/100 =2
Solving these two equations we get
x =150 , v = 300
And
x =133.33 , v = 200

Superset
The arrival time will be a positive real number based on the selection of one case.

Transaltion
In order to find the value, we need
1# another equation to select one case
2# one information to select one case

Statement analysis

St 1: for case 1, train A arrives at 4:30PM and train b arrives at 4;20pm
For case 2, train A arrives at 4:20 PM and train B arrives at 4:10PM INSUFFICIENT
St 2: Case 2 is rejected. HEnce train B arrives at 4:20PM. Option C
_________________

GMAT Mentors
Image

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1323
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 22 Mar 2017, 22:23
Bunuel wrote:
rohitgoel15 wrote:
Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?

(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Please help me know the difficulty level of this question. I was not able to solve it in even 5 mins :(


Let:
\(d\) be the distance between cities;
\(x\) be the rate of Train B.

"An hour later (so at 4:00PM), Train A passes Train B" --> before they pass each other A traveled 1 hour (4PM-3PM) and B traveled 1/6 hours (4PM-3:50PM).

"Combined travel time of the two trains is 2 hours" --> d/100(time to cover all distance for train A)+d/x(time to cover all distance for train B)=2 --> \(\frac{d}{100}+\frac{d}{x}=2\);

As before they pass A traveled 100 miles (1 hour at 100 miles per hour), then distance to cover for B after they pass is this 100 miles and as B traveled x*1/6 miles before they pass (1/6 hour at x miles per hour), then distance to cover for A after they pass is this x*1/6 miles --> \(100+\frac{x}{6}=d\);

So, we have:
\(\frac{d}{100}+\frac{d}{x}=2\) and \(100+\frac{x}{6}=d\).

Solving for \(d\) and \(x\)
\(d=150\) and \(x=300\);
OR:
\(d=\frac{800}{6}\approx{133.3}\) and \(x=200\).

(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient

(2) Says that \(d>140\) --> \(d=150\) --> \(x=300\), arrival time for B 4:20. Sufficient

Answer D.

P.S. This is definitely a hard (700+) question.

Hope it's clear.


The algebra is tough for me.

\(\frac{d}{100}+\frac{d}{x}=2\)

\(dx + 100d = 200x\)

\(100d = x(200-d)\) -----(1)

\(100 + \frac{x}{6}=d\)

\(600 + x = 6d\)

\(x = 6d - 600\) -----(2)

Substitute (1) into (2)

\(6d^2 - 1700d + 120000 = 0\)

\((d - 150)(6d - 800)=0\)

How to identify \((d - 150)(6d - 800)=0\) in a faster way? The algebra is complicated.

Dear Bunuel, There is two different solutions for Statement 1. Could you help to elaborate why it is sufficient for statement 1? Thank you. :-D

(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51214
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 22 Mar 2017, 22:43
ziyuen wrote:
Bunuel wrote:
rohitgoel15 wrote:
Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?

(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Please help me know the difficulty level of this question. I was not able to solve it in even 5 mins :(


Let:
\(d\) be the distance between cities;
\(x\) be the rate of Train B.

"An hour later (so at 4:00PM), Train A passes Train B" --> before they pass each other A traveled 1 hour (4PM-3PM) and B traveled 1/6 hours (4PM-3:50PM).

"Combined travel time of the two trains is 2 hours" --> d/100(time to cover all distance for train A)+d/x(time to cover all distance for train B)=2 --> \(\frac{d}{100}+\frac{d}{x}=2\);

As before they pass A traveled 100 miles (1 hour at 100 miles per hour), then distance to cover for B after they pass is this 100 miles and as B traveled x*1/6 miles before they pass (1/6 hour at x miles per hour), then distance to cover for A after they pass is this x*1/6 miles --> \(100+\frac{x}{6}=d\);

So, we have:
\(\frac{d}{100}+\frac{d}{x}=2\) and \(100+\frac{x}{6}=d\).

Solving for \(d\) and \(x\)
\(d=150\) and \(x=300\);
OR:
\(d=\frac{800}{6}\approx{133.3}\) and \(x=200\).

(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient

(2) Says that \(d>140\) --> \(d=150\) --> \(x=300\), arrival time for B 4:20. Sufficient

Answer D.

P.S. This is definitely a hard (700+) question.

Hope it's clear.


The algebra is tough for me.

\(\frac{d}{100}+\frac{d}{x}=2\)

\(dx + 100d = 200x\)

\(100d = x(200-d)\) -----(1)

\(100 + \frac{x}{6}=d\)

\(600 + x = 6d\)

\(x = 6d - 600\) -----(2)

Substitute (1) into (2)

\(6d^2 - 1700d + 120000 = 0\)

\((d - 150)(6d - 800)=0\)

How to identify \((d - 150)(6d - 800)=0\) in a faster way? The algebra is complicated.

Dear Bunuel, There is two different solutions for Statement 1. Could you help to elaborate why it is sufficient for statement 1? Thank you. :-D

(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient


Because of the first statement which says that that train B arrived before A. Only if x = 300, train B arrives before A but of x = 200 A arrives before B.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51214
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 22 Mar 2017, 22:44
ByjusGMATapp wrote:
Prompt analysis
Let the distance be x, speed of train B be v, t be the time taken after departure to meet train B
x = v/6 +100*1
x/v +x/100 =2
Solving these two equations we get
x =150 , v = 300
And
x =133.33 , v = 200

Superset
The arrival time will be a positive real number based on the selection of one case.

Transaltion
In order to find the value, we need
1# another equation to select one case
2# one information to select one case

Statement analysis

St 1: for case 1, train A arrives at 4:30PM and train b arrives at 4;20pm
For case 2, train A arrives at 4:20 PM and train B arrives at 4:10PM INSUFFICIENT
St 2: Case 2 is rejected. HEnce train B arrives at 4:20PM. Option C


Please note that the correct answer is D, not C. You posted two identical incorrect answers. Please read the whole thread before posting a reply. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 632
Location: India
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 09 Aug 2017, 20:11
Let the distance between New York and Boston be d miles. Let the speed of train B be s2

d/100 + d/s2 = 2. – (1)

Also, by 3:50, train A would have traveled (5/6)*100. So distance traveled between 3:50 to 4:00 is
d- (5/6) *100 = (100+s2) *1/6 -- (2)

From (1) and (2) we know we have two values of d and s2.
At this point we can guess especially if short of time, that statements (1) and (2) try to eliminate one of these values and hence D.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Manager
Manager
User avatar
S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 12 Aug 2017, 11:47
An easy way to look at the same problem especially for those who are not fond of math


Assuming total distance to be 150 miles

(For the graph please open the doc file attached with this post)



From first Statement
Since train B takes 10 minutes to cover 50 miles, it will take 20 minutes to cover remaining 100 miles. Thus total time taken by B is 30 minutes. Also train A takes 1hr (60 mins) to cover 100 miles, so it will take 30 minutes to cover remaining 50 miles. Thus total time taken by A is 90 minutes. Thus total time taken by both trains = 120 mins (2hrs).
Also train B is reaching earlier than train A
Assuming any other number like 140 or 125 for distance between two stations will either not lead to total time as 2 hours or will breach the condition of train B reaching
From second Statement
Since distance is greater than 140, 150 suites the situation.
Thus we can find the time at which train B reaches New York station from both statements alone.
Attachments

File comment: An easy way to look at the same problem especially for those who are not fond of math
A train leaves from NY to Boston.docx [12.1 KiB]
Downloaded 39 times

To download please login or register as a user


_________________

Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Intern
Intern
avatar
B
Joined: 21 Mar 2017
Posts: 39
Location: Zimbabwe
Concentration: General Management, Entrepreneurship
GMAT 1: 680 Q45 V38
GMAT 2: 750 Q49 V42
GPA: 3.3
WE: Accounting (Accounting)
GMAT ToolKit User Reviews Badge
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 22 Sep 2017, 20:04
VeritasPrepKarishma wrote:
Interesting question. I would like to share my thoughts on it. The first thing I notice is that the statements do not provide any concrete data. I cannot solve anything using them so most probably I will be able to get an answer from the data in the question stem but I will get multiple possible answers. The statements will probably help me choose one of them. (all a speculation based on the statements. The answer may be E) I know a quadratic gives me multiple answers.

Attachment:
Ques2.jpg

The diagram above incorporates the data given in the question stem. Let x be the distance from meeting point to Boston.

Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
Total time taken by both is 2 hrs. Already accounted for is 1hr + (1/6) hr
The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.

Time taken by train A to reach B + time taken by train B to reach NY = 5/6
x/100 + 100/6x = 5/6
3x^2 - 250x + 5000 = 0 (Painful part of the question)
x = 50, 33.33


(1) Train B arrived in New York before Train A arrived in Boston.
If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach NY = 1/3 hr
If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach NY = 1/2 hr
Since train B arrived first, x must be 50 and B must have arrived at 4:20. Sufficient.

(2) The distance between New York and Boston is greater than 140 miles.
x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.


Hi VeritasPrepKarishma. Thanks for the insightful wallkthrough. One question though. How do you solve 3x^2 - 250x + 5000 = 0.
_________________

Kudos if you like my response please

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8677
Location: Pune, India
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 25 Sep 2017, 20:26
streetking wrote:
VeritasPrepKarishma wrote:
Interesting question. I would like to share my thoughts on it. The first thing I notice is that the statements do not provide any concrete data. I cannot solve anything using them so most probably I will be able to get an answer from the data in the question stem but I will get multiple possible answers. The statements will probably help me choose one of them. (all a speculation based on the statements. The answer may be E) I know a quadratic gives me multiple answers.

Attachment:
Ques2.jpg

The diagram above incorporates the data given in the question stem. Let x be the distance from meeting point to Boston.

Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
Total time taken by both is 2 hrs. Already accounted for is 1hr + (1/6) hr
The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.

Time taken by train A to reach B + time taken by train B to reach NY = 5/6
x/100 + 100/6x = 5/6
3x^2 - 250x + 5000 = 0 (Painful part of the question)
x = 50, 33.33


(1) Train B arrived in New York before Train A arrived in Boston.
If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach NY = 1/3 hr
If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach NY = 1/2 hr
Since train B arrived first, x must be 50 and B must have arrived at 4:20. Sufficient.

(2) The distance between New York and Boston is greater than 140 miles.
x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.


Hi VeritasPrepKarishma. Thanks for the insightful wallkthrough. One question though. How do you solve 3x^2 - 250x + 5000 = 0.



\(3x^2 - 250x + 5000 = 0\)

\(3x^2 -150x - 100x + 5000 = 0\)

\(3x(x - 50) - 100(x - 50) = 0\)

\((x - 50)*(3x - 100) = 0\)

x = 50, 100/3

Here is a post on how to solve hard quadratic equations:
https://www.veritasprep.com/blog/2013/1 ... equations/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
User avatar
B
Joined: 03 Apr 2018
Posts: 37
Concentration: Strategy, Leadership
GMAT 1: 750 Q50 V41
Reviews Badge
Re: Train A leaves New York for Boston at 3 PM and travels at  [#permalink]

Show Tags

New post 07 Aug 2018, 19:00
amazing question... not sure if this can be done within 2 minutes if it pops up in the actual exam
GMAT Club Bot
Re: Train A leaves New York for Boston at 3 PM and travels at &nbs [#permalink] 07 Aug 2018, 19:00

Go to page   Previous    1   2   3   [ 51 posts ] 

Display posts from previous: Sort by

Train A leaves New York for Boston at 3 PM and travels at

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.