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

 It is currently 22 Oct 2019, 20:26

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

Anand starts from a point P towards point Q, where PQ = 90

Author Message
TAGS:

Hide Tags

Manager
Joined: 19 Oct 2010
Posts: 158
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

Updated on: 13 Jul 2013, 07:19
2
19
00:00

Difficulty:

65% (hard)

Question Stats:

67% (03:08) correct 33% (03:13) wrong based on 179 sessions

HideShow timer Statistics

Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A) (45/7) kmph
(B) (60/7) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph

_________________
petrifiedbutstanding

Originally posted by petrifiedbutstanding on 03 Sep 2011, 08:22.
Last edited by Bunuel on 13 Jul 2013, 07:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1571

Show Tags

03 Sep 2011, 08:58
12
3
petrifiedbutstanding wrote:
Found this exercise in a random book.

Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A). (45/7) kmph
(B). (60/7) kmph
(C). (40/7) kmph
(D). (30/7) kmph
(E). (65/7) kmph

Can someone help with this, please?

Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90-x) km

Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph

So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km

And between their first meeting point and second, they both together covered a distance of 2(90-x) km.

2x+3x=2(90-x)
5x=180-2x
7x=180
x=180/7 km

Anand's speed=x/3=180/(3*7)=60/7 kmph

Ans: "B"
_________________
General Discussion
Senior Manager
Joined: 08 Nov 2010
Posts: 272

Show Tags

04 Sep 2011, 10:00
fluke wrote:
petrifiedbutstanding wrote:
Found this exercise in a random book.

Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A). (45/7) kmph
(B). (60/7) kmph
(C). (40/7) kmph
(D). (30/7) kmph
(E). (65/7) kmph

Can someone help with this, please?

Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90-x) km

Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph

So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km

And between their first meeting point and second, they both together covered a distance of 2(90-x) km.

2x+3x=2(90-x)
5x=180-2x
7x=180
x=180/7 km

Anand's speed=x/3=180/(3*7)=60/7 kmph

Ans: "B"

Nice solution. I made it much more complicated...

I used - 3A=2R
8R=90+x
9A=90-x

solving giving the same result - but i guess it took me longer than to you and increased my chances to make mistakes...
_________________
Manager
Joined: 04 Jun 2011
Posts: 128

Show Tags

04 Sep 2011, 10:08
yup nice and easy one fluke!! kudos for the wonderfully solving the problem in 3 steps
Intern
Status: Dreaming High
Joined: 24 Apr 2011
Posts: 48
Location: India
Concentration: Operations, Strategy
GMAT 1: 720 Q50 V36
GPA: 3.28
WE: Project Management (Manufacturing)

Show Tags

04 Sep 2011, 10:30
2
Speed of Anand =a
'" Ram=r
Till Anand and Ram meets, Anand travels for 3 hrs, and Ram trvels for 2 HRs
When Two people meet, the distance travelled by them is equal
=>> 3a = 2r
which gives r = 3a/2------------(i)
Now for next 6 hrs, Anand travels 6a Kms and Ram trvls 6r Kms.

Refer the pic:
....(3a)......||...........(6a)..................|||...............
P|_________||______________________|||_________Q
....(2r)......||..............................(6r)....................

The (6r) covers the distance from (|| to Q)plus( Q to ||| )
PQ = 90
2PQ = 180
3a + 6a + 6r + 2r = 180
9a + 8r = 180
9a + 8*3a/2 = 180 -----using (i)
9a + 12a = 180
a = 180/21 = 60/7

From this
_________________
[caption=]Remember: Anything that can go wrong, will go wrong.[/caption]
SVP
Joined: 24 Jul 2011
Posts: 1881
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740

Show Tags

04 Sep 2011, 11:41
3
Let a be Anand's speed and r be Ram's speed.When Ram and Anand meet for the first time, distance travelled by them is the same
=> a(3) = r(2)
When Ram and Anand meet for the second time, they have travelled twice the distance PQ, or 180 km, together
=> a(9) + r(8) = 180

Solving these equations for a, we get a = 180/21 = 60/7 km/hr
=>Option (B)
_________________

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Manager
Joined: 19 Oct 2010
Posts: 158
Location: India
GMAT 1: 560 Q36 V31
GPA: 3

Show Tags

07 Sep 2011, 03:01
Thank you, fluke and GynaOne. Really simple solutions!
_________________
petrifiedbutstanding
Intern
Joined: 20 Jul 2011
Posts: 6
Location: India
GPA: 3.12
WE: Information Technology (Consulting)

Show Tags

07 Sep 2011, 07:23
Couldn get it the first time
Took more than 5 min to solve.
After looking at the solution it looked easy but I was stumped
Have a small doubt.. On GMAT wats the probability of facing these kind of questions ??
And at what level??

-cheers
_________________
Maverick%^%^
Intern
Joined: 06 Dec 2012
Posts: 23
GMAT 1: 510 Q46 V21
GPA: 3.5
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

03 Oct 2013, 10:40
why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?
Intern
Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
Schools: CBS '18 (M)
GMAT 1: 770 Q51 V45
GPA: 3.36
WE: Analyst (Health Care)
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

03 Oct 2013, 14:26
1
I solved it like this:

Let R = Ram's speed
A = Anand's speed

Since it took Ram 2 hours to cover the same distance as Anand did in 3 hours we know

2R = 3A
R = (3/2)A

We know they don't meet again for another 6 hours, at which point Anand will have been traveling for 9 hours to a distance I'll call "D". Ram will have been traveling for only 8 hours when he reaches D and the total distance he will have traveled is 90 + (90 - D) = 180 - D

So:

9A = D
8R = 180 - D or 180 - 8R = D

180 - 8R = 9A

Substitute for R

180 - 8(3/2)A = 9A
180 - 12A = 9A
180 = 21A
60/7 = A
Current Student
Joined: 15 Sep 2013
Posts: 10
Schools: Sloan '19 (A\$)
GMAT 1: 700 Q46 V40
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

06 Oct 2013, 06:19
sunny3011 wrote:
why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?

Same question: Why is it 2(90-x)? I understand why we need the first (90-x), but why is it assumed that they meet at the same point X when they're headed back?
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

17 Oct 2013, 04:39
2
1
pauc wrote:
sunny3011 wrote:
Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A) (45/7) kmph
(B) (60/7) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph

why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?

Same question: Why is it 2(90-x)? I understand why we need the first (90-x), but why is it assumed that they meet at the same point X when they're headed back?

Look at the diagram below:
Attachment:

Untitled4.png [ 2.58 KiB | Viewed 3088 times ]
Blue dot is the second meeting point.

In blue is the distance covered by Anand after the first meeting.
In green is the distance covered by Ram after the first meeting.

Their sum is twice 90-x.

Hope it's clear.
_________________
Manager
Joined: 15 Aug 2013
Posts: 50
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

17 Oct 2013, 09:00
6
1
Here is a quick approach- since we know the time taken by anand : time taken by ram (same distance when they meet after 3 hrs) = 3 : 2. therefore, ratio of their speed= 2 : 3.
Let speed be 2x, 3x.
Now in three hours distance covered = 6x. remaining 90-6x covered twice in 6 hours.
=> 12x + 18x = 2(90-6x) giving 2x (remember this is the speed of anand and not just x) = 60/7
Manager
Joined: 26 Sep 2013
Posts: 184
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

17 Oct 2013, 09:56
I don't get this problem at all; you don't know how long it takes Ram to reach the end point and then turn back, so you can't calculate anything for certain...there's too many variables here.
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

17 Oct 2013, 09:58
AccipiterQ wrote:
I don't get this problem at all; you don't know how long it takes Ram to reach the end point and then turn back, so you can't calculate anything for certain...there's too many variables here.

Check solutions above. You can use only one variable to solve.
_________________
Director
Joined: 17 Dec 2012
Posts: 626
Location: India
Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

24 Jun 2014, 22:05
Since Anand takes 3 hrs to travel the distance that Ram travels in 2 hrs their speed is in the ratio 2:3. We also know s1=(90-x)/9 and s2=(90+x)/8 where s1 and s2 are the speed of Anand and Ram resp.
(90-x) /9 / (90+x)/8 = 2/3
From the above equations we get s1=60/7
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Non-Human User
Joined: 09 Sep 2013
Posts: 13412
Re: Anand starts from a point P towards point Q, where PQ = 90  [#permalink]

Show Tags

31 Jan 2018, 17:00
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: Anand starts from a point P towards point Q, where PQ = 90   [#permalink] 31 Jan 2018, 17:00
Display posts from previous: Sort by