GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Apr 2020, 01:39

### 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

# A left P for Q at 10:00 am. At the same time B left Q for P.

Author Message
TAGS:

### Hide Tags

Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 225
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

27 Aug 2015, 18:17
3
12
00:00

Difficulty:

75% (hard)

Question Stats:

59% (03:00) correct 41% (02:54) wrong based on 94 sessions

### HideShow timer Statistics

A left P for Q at 10:00 am. At the same time B left Q for P. After they met at a point on the way, A took 24 mins to reach Q and B took 54 mins to reach P. At what time did they meet?

A. 10:35 am
B. 10:36 am
C. 10:37 am
D. 10:38 am
E. 10:39 am
CEO
Joined: 20 Mar 2014
Posts: 2542
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

27 Aug 2015, 18:37
2
3
arhumsid wrote:
A left P for Q at 10:00 am. At the same time B left Q for P. After they met at a point on the way, A took 24 mins to reach Q and B took 54 mins to reach P. At what time did they meet?

A. 10:35 am
B. 10:36 am
C. 10:37 am
D. 10:38 am
E. 10:39 am

Let S be the total distance between P and Q

Let Va and Vb be the speeds of A and B respectively.

Let t be the meeting time.

Per the question, Va*t+Vb*t = s ...(1)

Also, Vb*t+Vb*54 = s ---> Vb = s/(t+54) ....(2)

Similarly, Va = s/(t+24) ....(3)

Substituting values of Va and Vb from 2 and 3 respectively into 1 we get,

t = 36 minutes.

Thus they met at 10:00 AM + 36 minutes = 10:36 AM.

##### General Discussion
Manager
Status: single
Joined: 19 Jan 2015
Posts: 80
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

27 Aug 2015, 18:53
2
2
hi here we can use , in Time and distance if both trains start at the same time
and travelled in opposite directions.
when you want to find time of both trains to meet,
we can multiply both the times and take square root of it.

Here one train reached at 54mins and another trains reached at 24 mins.

Multiply both times 54*24=1296.
square root of 1296 is 36mins.

from 1296 we dont need square root also because unit digit ends in 6 . only the number unit ends in 6 only have that square.

We can use and apply logic to save time in GMAT.

So option B is correct.
Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 225
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

27 Aug 2015, 20:53
Psiva00734 wrote:
hi here we can use , in Time and distance if both trains start at the same time
and travelled in opposite directions.
when you want to find time of both trains to meet,
we can multiply both the times and take square root of it.

By Time you mean, The time they took after meeting eachother? Does this hold true always?
VP
Joined: 07 Dec 2014
Posts: 1242
A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

28 Aug 2015, 15:22
1
4
Because they derive from the same distance, the ratio between A's pre-meeting time (t)
and total time (t+24) is equal to the ratio between B's post-meeting time (54) and total
time (t+54).
t/t+24=54/t+54
t^2=1296
t=36
Board of Directors
Joined: 17 Jul 2014
Posts: 2456
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

06 Feb 2016, 09:43
I don't get it...
anyone can explain, maybe with graphs how to solve it?
Intern
Joined: 14 Jul 2015
Posts: 20
GMAT 1: 680 Q44 V40
GMAT 2: 710 Q49 V37
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

07 Feb 2016, 22:39
3
mvictor wrote:
I don't get it...
anyone can explain, maybe with graphs how to solve it?

Do you need an explanation for Gracie's solution?

If you need an explanation for Gracie's solution, since I wanted to know how her solution ticked, I quickly analyzed it from the ground up:

The first/long section is x, and the second/narrow section is y. The point about 2/3 through is where A and B met. A spent 24 minutes in section y, and B spent 54 minutes in section x.

P |-----------------------|------------| Q

1. Let's state the central idea Gracie's solution is built around: the distance A has to travel is the same distance B has to travel. Please keep this in the back of your mind for the next few steps.

2. For A, we know the time he spent in section y but not section x. As such, we can say that A spent $$\frac{time_x}{{time_x + 24}}$$% of his travel time covering section x, and $$\frac{24}{{time_x + 24}}$$% of his travel time covering section y.

3. For B, we know the time he spent in section x but not section y. As such, we can say that B spent $$\frac{54}{{time_y + 54}}$$% of his travel time covering section x, and $$\frac{time_y}{{time_y + 54}}$$% of his travel time covering section y.

4. Since A and B are traveling at a constant speed (this is an assumption- be extremely careful with assumptions), we know that both will share the same percent of their time in each section. As such, if we select a section, the amount of time each party spent in that section will be equal. Let's use section x going forward.

5. From (4), we have $$\frac{t}{{t + 24}} = \frac{54}{{t + 54}}$$

6. $$t * (t + 54) = 54 * (t + 24)$$

7. $$t^2 + 54t = 54t + 54*24$$

8. $$t^2 = 1296$$

9. $$t = 36$$

10. Since A spent t minutes traveling before meeting B, and t = 36, our answer must be 10:36, or B.

If anyone sees any errors in my reasoning, please let me know.
Manager
Joined: 03 Dec 2014
Posts: 88
Location: India
GMAT 1: 620 Q48 V27
GPA: 1.9
WE: Engineering (Energy and Utilities)
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

07 Feb 2016, 23:09
Engr2012 wrote:
arhumsid wrote:
A left P for Q at 10:00 am. At the same time B left Q for P. After they met at a point on the way, A took 24 mins to reach Q and B took 54 mins to reach P. At what time did they meet?

A. 10:35 am
B. 10:36 am
C. 10:37 am
D. 10:38 am
E. 10:39 am

Let S be the total distance between P and Q

Let Va and Vb be the speeds of A and B respectively.

Let t be the meeting time.

Per the question, Va*t+Vb*t = s ...(1)

Also, Vb*t+Vb*54 = s ---> Vb = s/(t+54) ....(2)

Similarly, Va = s/(t+24) ....(3)

Substituting values of Va and Vb from 2 and 3 respectively into 1 we get,

t = 36 minutes.

Thus they met at 10:00 AM + 36 minutes = 10:36 AM.

the easiest way of doing this question :

meeting time T= sqrt of 24x36 =36
so, they will meet at 10.36 min form start.
Board of Directors
Joined: 17 Jul 2014
Posts: 2456
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

08 Feb 2016, 08:32
Beixi88 wrote:
mvictor wrote:
I don't get it...
anyone can explain, maybe with graphs how to solve it?

Do you need an explanation for Gracie's solution?

If you need an explanation for Gracie's solution, since I wanted to know how her solution ticked, I quickly analyzed it from the ground up:

The first/long section is x, and the second/narrow section is y. The point about 2/3 through is where A and B met. A spent 24 minutes in section y, and B spent 54 minutes in section x.

P |-----------------------|------------| Q

1. Let's state the central idea Gracie's solution is built around: the distance A has to travel is the same distance B has to travel. Please keep this in the back of your mind for the next few steps.

2. For A, we know the time he spent in section y but not section x. As such, we can say that A spent $$\frac{time_x}{{time_x + 24}}$$% of his travel time covering section x, and $$\frac{24}{{time_x + 24}}$$% of his travel time covering section y.

3. For B, we know the time he spent in section x but not section y. As such, we can say that B spent $$\frac{54}{{time_y + 54}}$$% of his travel time covering section x, and $$\frac{time_y}{{time_y + 54}}$$% of his travel time covering section y.

4. Since A and B are traveling at a constant speed (this is an assumption- be extremely careful with assumptions), we know that both will share the same percent of their time in each section. As such, if we select a section, the amount of time each party spent in that section will be equal. Let's use section x going forward.

5. From (4), we have $$\frac{t}{{t + 24}} = \frac{54}{{t + 54}}$$

6. $$t * (t + 54) = 54 * (t + 24)$$

7. $$t^2 + 54t = 54t + 54*24$$

8. $$t^2 = 1296$$

9. $$t = 36$$

10. Since A spent t minutes traveling before meeting B, and t = 36, our answer must be 10:36, or B.

If anyone sees any errors in my reasoning, please let me know.

Thanks, your explanation does clear things up. I did not understand the reasoning behind the equation written by Gracie.
I understood that:
1. A was travelling faster than B
2. point of intersection is closer to Q

yet, I did not see how to solve further this point.
Thanks one more time..would definitely remember this case. Kudos for you
Intern
Joined: 01 Jan 2016
Posts: 27
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

12 Aug 2017, 21:40
Psiva00734 wrote:
hi here we can use , in Time and distance if both trains start at the same time
and travelled in opposite directions.
when you want to find time of both trains to meet,
we can multiply both the times and take square root of it.

Here one train reached at 54mins and another trains reached at 24 mins.

Multiply both times 54*24=1296.
square root of 1296 is 36mins.

from 1296 we dont need square root also because unit digit ends in 6 . only the number unit ends in 6 only have that square.

We can use and apply logic to save time in GMAT.

So option B is correct.

Would be great if someone can explain how this method works
Director
Joined: 14 Nov 2014
Posts: 580
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

12 Aug 2017, 23:36
1
theperfectgentleman wrote:
Psiva00734 wrote:
hi here we can use , in Time and distance if both trains start at the same time
and travelled in opposite directions.
when you want to find time of both trains to meet,
we can multiply both the times and take square root of it.

Here one train reached at 54mins and another trains reached at 24 mins.

Multiply both times 54*24=1296.
square root of 1296 is 36mins.

from 1296 we dont need square root also because unit digit ends in 6 . only the number unit ends in 6 only have that square.

We can use and apply logic to save time in GMAT.

So option B is correct.

Would be great if someone can explain how this method works

lets take D traveled by A ....and D1 traveled by B....Time traveled is " T "
D/T = S(a) =D = T*S(a)-----------1
D1/T = S(b) =D1 = T*S(b)----------2

now A need 24 min to travel what B has already covered ....(as they meet in a common point)
So D1/24 = S(a)...
substituting 2 here ...
T*S(b)/S(a) = 24 ------------3

similarly for B ...
D/54 = S(b)
substituting 1 here
T*S(a)/S(b) = 54 ------------4

if we multiply 3 and 4 we will get ..
T^2 = 24 * 54
T = 36
Non-Human User
Joined: 09 Sep 2013
Posts: 14468
Re: A left P for Q at 10:00 am. At the same time B left Q for P.  [#permalink]

### Show Tags

09 Feb 2020, 09:47
1
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: A left P for Q at 10:00 am. At the same time B left Q for P.   [#permalink] 09 Feb 2020, 09:47
Display posts from previous: Sort by