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

 It is currently 18 Oct 2019, 16:38 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

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.  Two friends, Tanaya and Stephen were standing together. Tanaya begins

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

Hide Tags

Manager  Joined: 14 Oct 2014
Posts: 51
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

7 00:00

Difficulty:   65% (hard)

Question Stats: 67% (02:51) correct 33% (03:02) wrong based on 117 sessions

HideShow timer Statistics

Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Originally posted by manishbhusal on 07 Apr 2015, 10:30.
Last edited by Bunuel on 07 Apr 2015, 10:44, edited 1 time in total.
Renamed the topic and edited the question.
Director  Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

2
3
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min
General Discussion
Manager  Joined: 17 Mar 2015
Posts: 115
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

2
t1 - time it takes to cover the same distance tanya covered.
$$3 + t1*3 = 9*t1, t1 = 1/2$$
t2 - time it takes to cover twice of the distance Tanya covered
$$2*(3+t2*3) = 9*t2, t2 = 2$$
$$t2 - t1 = 1.5 = 90$$ minutes, answer C.
Manager  Joined: 14 Oct 2014
Posts: 51
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

Lucky2783 wrote:
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min

Would you mind telling how you got the second equation. I understood the L.H.S part i.e (2x+6) is twice the distance of what tanya had covered.so time taken = (2x+6)/9, but i couldn't understand the R.H.S part of second equation . i.e how we got x/3 and how (2x+6)/9 is equal to x/3.

Thanks
Manish
Director  Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

1
manishbhusal wrote:
Lucky2783 wrote:
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min

Would you mind telling how you got the second equation. I understood the L.H.S part i.e (2x+6) is twice the distance of what tanya had covered.so time taken = (2x+6)/9, but i couldn't understand the R.H.S part of second equation . i.e how we got x/3 and how (2x+6)/9 is equal to x/3.

Thanks
Manish

Hi Manish,

Lets assume that Tanya walked Y Miles when Stephen ran twice the distance she walked.

stephen had to run 2*(Y+3) .

2*(Y+3) /9 = Y/3 (tanya walked only Y Miles when stephen started to run )

hope it is clear .
Attachments gmatclub.jpg [ 82.78 KiB | Viewed 2235 times ]

Manager  Joined: 19 Mar 2015
Posts: 57
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

3
Assume Tanya travels for t hours.
So, Stephen travels for (t-1) hours

Since distance is the same
3t = 9(t-1)
t = 1.5 hours
So, Stephen travels for 0.5 hours to travel the same distance as Tanya.

Now, Stephen is supposed to travel twice the distance.
Again, suppose Tanya travels for t hours
So, Stephen travels for (t-1) hours
Since Stephen travels twice the distance as Tanya does,
9(t-1) = 2*3t
t = 3 hours
So, Stephen travels for 2 hours to travel twice the distance as Tanya.

So, difference = 2 - 0.5 = 1.5 hours = 90 minutes.
Board of Directors P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

1
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

oh nice..that's a good brain killer.

after 1 hour, tanya traveled for 3 miles. Stephen 0.
after 2 hours, tanya - 6 miles, stephen -9 miles
after 3 hours, tanya 9 miles, stephen - 18 miles.
ok, so stephen needs 2 hours to cover twice the distance tanya has walked.

now, time needed for stephan to cover the same distance tanya has walked.
1 hour -> tanya 3, stephen -0.
we know the rates of each.
in 20 minutes, tanya walks 1 miles, stephen 3.
so after 1h 20 mins, tanya walked 4 miles. stephen in 20 mins - 3 miles.
so if 20 mins for tanya 1 mile and for stephen 3, then in 10 mins, tanya will walk 0.5 miles and stephen 1.5
so...after another 10 mins, tanya 4.5 miles, stephen 4.5 miles.
we can see that stephen needs 30 mins to cover the same distance that tanya has covered.

now, 30-120=-90. since we are asked for the POSITIVE difference, -90*-1 = 90 mins.
VP  P
Joined: 07 Dec 2014
Posts: 1224
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

let t=Stephen's time
t+1=Tanaya's time
equation 1: 9t=3(t+1)
t=1/2 hour=30 minutes
equation 2: 9t=(2)(3)(t+1)
t=2 hours=120 minutes
120-30=90 minutes
Manager  B
Joined: 09 Aug 2017
Posts: 59
Location: United States
Concentration: Technology
GMAT 1: 640 Q44 V33 GMAT 2: 630 Q47 V29 WE: Research (Investment Banking)
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

I'll be honest this is a really poorly written question and I have to wonder if this was written by a native English speaker because what the question is asking for isn't an answer. The positive difference between the distance she's covered and twice the distance she's covered is going to change based on how long she's walking. We don't know how long she's been walking. This question needs to be rewritten.
_________________
I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

Also, I appreciate any kudos.
Non-Human User Joined: 09 Sep 2013
Posts: 13262
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins   [#permalink] 18 May 2019, 11:59
Display posts from previous: Sort by

Two friends, Tanaya and Stephen were standing together. Tanaya begins

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

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