a doubt on the answer to Q14 in 3rd MGMAT CAT test

[Maria]

I did the 3rd MGMAT CAT test, and there is a problem in quantitive I have doubt on the answer. Question 14-Data sufficient.

Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?

(1) Bob’s average speed for the entire journey was 4 mph.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

The answer: Satement 2 alone is sufficient, but statement 1 alone is not sufficient.
According to the explaination , 32m is the time that Wendy wait for Bob at the restaurant.

If I understand correctly, 32 minutes is the time Bob spent on his way return to their home in the half way and then the full journey to the restaurant; During this time Wendy continue heading for the restaurant , and appearantly arrive earlier than Bob. The actual time Wendy wait for Bob at the restaurant should be 32 minutes minus the time Wendy spend for the rest half of the journey to the restaurant, since she still has half a way to go when Bob return for home.

Given above, I consider statement 1 and 2 will be sufficient to answer the question , while neither of each alone is sufficient, Correct answer should be C.
Assume T is the time for both of them travel half of the way at speed 3PMH, thus
4X(T+32/60)=3*2T*2
T=8/30
The time Wendy wait for Bob at the restaurant should be
32/60-8/30=16/60, in other word 16 minutes

Have I misread the conditions if the descrepancies do not exist ?

[UPA]

I did the 3rd MGMAT CAT test, and there is a problem in quantitive I have doubt on the answer. Question 14-Data sufficient.

Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?

(1) Bob’s average speed for the entire journey was 4 mph.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

The answer: Satement 2 alone is sufficient, but statement 1 alone is not sufficient.
According to the explaination , 32m is the time that Wendy wait for Bob at the restaurant.

If I understand correctly, 32 minutes is the time Bob spent on his way return to their home in the half way and then the full journey to the restaurant; During this time Wendy continue heading for the restaurant , and appearantly arrive earlier than Bob. The actual time Wendy wait for Bob at the restaurant should be 32 minutes minus the time Wendy spend for the rest half of the journey to the restaurant, since she still has half a way to go when Bob return for home.

Given above, I consider statement 1 and 2 will be sufficient to answer the question , while neither of each alone is sufficient, Correct answer should be C.
Assume T is the time for both of them travel half of the way at speed 3PMH, thus
4X(T+32/60)=3*2T*2
T=8/30
The time Wendy wait for Bob at the restaurant should be
32/60-8/30=16/60, in other word 16 minutes

Have I misread the conditions if the descrepancies do not exist ?

bob's walking time alone = x
bob's walking time with wendy = y
so x - y = 32 minuetssince it takes wendy to reach to resturant x minuets.
so wendy has to wait for (x - y) minuets.
therefore B alone is suff..

[Spencer]

Maria, I'm with you!

Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?

(1) Bob’s average speed for the entire journey was 4 mph.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.


1) This is insufficient because we don't know how long the total distance is.

We can figure out Bob's rate for each leg of the journey but as long as we don't know a total distance, the time she waited will never be concrete.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

Bob's Journey consisted of 4 trips. (1 with Wendy halfway, 1 back home, 1 to the half way point, and 1 to the restaurant). He traveled the distance from the house to the restaurant twice.

If the total distance to the restaurant was 30 miles:

Wendy would've made it in 10 hours.

Bob walked for 5 hours with Wendy and traveled 45 miles to go back home and to the restaurant in the 32 minutes (the time he was alone). He would've beat Wendy to the restaurant because it would take her 5 more hours to walk the distance that Bob covered in less then 1 hour.

Now if the total distance to the restaurant was 3 miles:

Wendy would've made it in one hour.

Bob walked for 30 minutes with her and then it took him 32 minutes to go home and back to the restaurant. So Wendy would've been waiting for 2 minutes.


I don't see how B alone is sufficient to answer this question. Help!

[Spencer]

::::::::::PAGING STACEY::::::::::::::

[Guest]

I'll say upfront that the answer is correct. This is a tricky problem that takes advantage of a hidden symmetry.

If we agree up front that (1) is insufficient by itself let's move on to (2)

Let D = distance from home to restaraunt
Let S = Speed of Bob after he leaves Wendy

Then, remembering the Time = Distance/Speed, (2) tells us that (D/2)/3 = (3D/2)/S -(32/60). That is, the time it took him to walk halfway at 3mph is 32 minutes less than the time it took Bob to walk half way home then all the way back to the restaurant. So, for example, if D =12 then it took him two hours to reach the halfway point at 3 mph and 2hrs 32min to walk 18 miles at an average speed of 7.1mph (ok, he jogged). But this is a lot more work than you need to do.

The key insight is to realize that Wendy will take the same amount of time to walk the last halfway to the restaurant as she and Bob took to walk the first half. Whereas Bob will take 32 minutes longer to run home and then all the way back to the restraunt. So if it takes them 1 hour to walk halfway, then Wendy will get the the restraunt after another hour and Bob will get there after 1 hr and 32 min. If it takes them 30 minutes to get half way, then wendy will get to the restraunt after another 30 minutes and bob will take 30+32 = 62 minutes to get there. In all cases wendy waits 32 minutes, so (2) is sufficient to answer the question, even though you have no idea how far it is from home to restaraunt or how fast Bob walks once he leaves Wendy.

I did the 3rd MGMAT CAT test, and there is a problem in quantitive I have doubt on the answer. Question 14-Data sufficient.

Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?

(1) Bob’s average speed for the entire journey was 4 mph.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

The answer: Satement 2 alone is sufficient, but statement 1 alone is not sufficient.
According to the explaination , 32m is the time that Wendy wait for Bob at the restaurant.

If I understand correctly, 32 minutes is the time Bob spent on his way return to their home in the half way and then the full journey to the restaurant; During this time Wendy continue heading for the restaurant , and appearantly arrive earlier than Bob. The actual time Wendy wait for Bob at the restaurant should be 32 minutes minus the time Wendy spend for the rest half of the journey to the restaurant, since she still has half a way to go when Bob return for home.

Given above, I consider statement 1 and 2 will be sufficient to answer the question , while neither of each alone is sufficient, Correct answer should be C.
Assume T is the time for both of them travel half of the way at speed 3PMH, thus
4X(T+32/60)=3*2T*2
T=8/30
The time Wendy wait for Bob at the restaurant should be
32/60-8/30=16/60, in other word 16 minutes

Have I misread the conditions if the descrepancies do not exist ?

[RonPurewal]

take statement (2) alone:
let's say X minutes is the time that wendy and bob walk together.
then, because they part ways at the exact halfway point, wendy walks X more minutes before arriving at the restaurant.
bob walks alone for 32 more minutes than with wendy; in other words, bob walks for X + 32 minutes.
therefore, the time wendy waits at the restaurant is
(time bob walks alone) - (time both of them are walking alone)
= (X + 32) - X
= 32

sufficient!

this is essentially the same solution posted by the poster directly above me, but in more concise terms.

tricky tricky!

[Spencer]

take statement (2) alone:
let's say X minutes is the time that wendy and bob walk together.
then, because they part ways at the exact halfway point, wendy walks X more minutes before arriving at the restaurant.
bob walks alone for 32 more minutes than with wendy; in other words, bob walks for X + 32 minutes.
therefore, the time wendy waits at the restaurant is
(time bob walks alone) - (time both of them are walking alone)
= (X + 32) - X
= 32

sufficient!

this is essentially the same solution posted by the poster directly above me, but in more concise terms.

tricky tricky!

I disagree with you.

Using your formula if X=The number of minutes they walk together, then Wendy's time is 2X. So lets say X=30

Wendy's time for the trip is 60 minutes (1 hour) and the total distance is 1 mile because she went 3mph.
Bob would've walked 30 minutes with Wendy and an additional 32 alone making his total time 62 minutes and her time 60 minutes. Therefore she waiting 2 minutes for him.

Since X=The number of minutes they walk together, and Wendy's time is 2X. Lets say X=60

Wendy's time for the trip is 120 minutes (2 hours) and the total distance is 6 miles. Bob spent 60 minutes walking with Wendy and 32 minutes walking alone. So his total trip time is 92 minutes and Wendy would've waited 28 minutes for him.

So in one case we have a 2 minute wait and in another we have a 28 minute wait. And that is why I believe this answer is insufficient.

Please explain to me why this is wrong




If Wendy and Bob walked half the distance in

[Spencer]

And also note that it says, "Bob is traveling at a new constant speed".

[StaceyKoprince]

Bob doesn't walk alone for 32 minutes. He spends 32 minutes MORE walking alone than he spent walking with Wendy.

So if they walk 30 minutes together for the first half, then he walks 30+32 minutes while walking alone.
If they walk 60 minutes together, then he walks 60+32 alone.

[GMAT Fever]

If we agree up front that (1) is insufficient by itself let's move on to (2)

I did this problem by adding in numbers for the distance. I took the 9 session course and I was taught that in most of these distance problems if distance isnt given you can add one yourself. After reviewing this thread it seems that this is not the case. Can someone explain to me, when and why you should input a distance value when solving for the time traveled??

Let me explain what I did for statement 1 and why I thought is was sufficient:

I created a double RTD chart for Bob and Wendy. I inputted 4 mph and 3 mph for Bob and Wendy's rates respectively.

Now for the distance I inputted 12 miles (I remember from the class they advised picking easy numbers that could be divisible by the rates) for Wendy's distance.

Then after I drew out the distance, it stated that Bob traveled halfway (6 miles) + back home (6 miles) + entire distance from home to the restaurant (12 miles) = (Total of 24 miles)

So from here I was able to calculate the the time for Wendy and Bob to travel their distances - 4 hours and 6 hours.

So am I not supposed to input distances for these types of questions? If not when are you supposed to, are their specific types of distance problems when you are and are not supposed to do this?

Thanks!

[RonPurewal]

If we agree up front that (1) is insufficient by itself let's move on to (2)

I did this problem by adding in numbers for the distance. I took the 9 session course and I was taught that in most of these distance problems if distance isnt given you can add one yourself. After reviewing this thread it seems that this is not the case. Can someone explain to me, when and why you should input a distance value when solving for the time traveled??

Let me explain what I did for statement 1 and why I thought is was sufficient:

I created a double RTD chart for Bob and Wendy. I inputted 4 mph and 3 mph for Bob and Wendy's rates respectively.

Now for the distance I inputted 12 miles (I remember from the class they advised picking easy numbers that could be divisible by the rates) for Wendy's distance.

Then after I drew out the distance, it stated that Bob traveled halfway (6 miles) + back home (6 miles) + entire distance from home to the restaurant (12 miles) = (Total of 24 miles)

So from here I was able to calculate the the time for Wendy and Bob to travel their distances - 4 hours and 6 hours.

So am I not supposed to input distances for these types of questions? If not when are you supposed to, are their specific types of distance problems when you are and are not supposed to do this?

Thanks!

well
if you're going to plug in numbers on these sorts of problems, you have to TRY MORE THAN ONE NUMBER / SET OF NUMBERS.

this should be obvious when you consider it from the standpoint of DATA SUFFICIENCY, which is the problem type considered here. remember: what is the point of data sufficiency?
the point of data sufficiency is to determine whether the given information is enough to determine ONE AND ONLY ONE VALUE for the quantity in question.
obviously, if you only input one number / set of numbers, you're only going to get one answer. using that logic, you're going to think that EVERY statement is sufficient, all the time!
the deal is you have to plug in multiple values. if you arrive at different answers - even two different answers - then you have shown that the information is insufficient, and there's no need to plug in further numbers. if you keep getting the same value over and over again, then you can take that to mean that the information is sufficient.