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# A certain city owns 298 buses, whose routes are divided into

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A certain city owns 298 buses, whose routes are divided into [#permalink]

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21 Jun 2011, 07:03
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A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64
[Reveal] Spoiler: OA

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21 Jun 2011, 07:09
My answer is A but looks like the answer choice is E. Can you please explain. The first question does provide the ratio and the total of the buses in the garage with which we can solve the equation.

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21 Jun 2011, 07:18
(1)

One Possibility:

4x + 6x + 7x + 26 = 298

=> 17x = 272

=> x = 16

So # of green buses = s = 16 * 7 = 112

Other possibility - q = 4, r = 6, s = 7

So s can be 7 as well
InSufficient

(2)

q gives us only the number of buses in blue zone, but no information about buses in grren zone

Insufficient

(1) + (2)

q = 64, then r = 6/4 * 64 = 96, and s = 7/4 * 64 = 112

Total = 64 + 96 + 112 + 26 = 298

Sufficient

Are you sure the OA is E ?
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21 Jun 2011, 07:23
The OA is E

but i disagree i got C as well it might be a TYPO then

thanks!
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21 Jun 2011, 07:46
rxs0005 wrote:
A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64

1) This is clearly no A because we did not have proportion of the bases in guarage to other. Insuff
2) q=64 / we have no relationtion with other type

1) + 2)
Give as q/s=4/7, from here 64/s=4/7. s = 64*7/4=16*7=112

I dont understand wy the correct answer is E

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08 Aug 2011, 00:45

Form statement A, I am not finding the second possibility suggested by subhash

There are 26 busses in the garage, so at the time of division, there are only 298-26 bussed available to be divided among the 3 regions

so x= 16. With that we can arrive at the solution? whats the catch here?

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08 Aug 2011, 01:08
manishgeorge wrote:

Form statement A, I am not finding the second possibility suggested by subhash

There are 26 busses in the garage, so at the time of division, there are only 298-26 bussed available to be divided among the 3 regions

so x= 16. With that we can arrive at the solution? whats the catch here?

Answer should be "A" unless Kaplan goes like: hehe.. tricked ya!!! I didn't tell you that buses can also be in the depots and bus stations; in which case, it should be "E".
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09 Aug 2011, 00:26
manishgeorge wrote:
There are 26 busses in the garage, so at the time of division, there are only 298-26 bussed available to be divided among the 3 regions

so x= 16. With that we can arrive at the solution? whats the catch here?

ya i thought with x=16 we can arrive at solution hence answer should be A. What's the catch?
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11 Aug 2011, 00:15
OA has to be A.
with the 2nd option the buses don't add up to 298 unless and un till buses are somewhere else,as suggested by Fluke.
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03 Nov 2011, 11:17
Should be A, ratio 4:6:7 cant be reduced.

298-26= 272
272/17= 16
16*7= 112

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04 Nov 2011, 03:37
Should be A .

Question clearly states that q + r + s + t = 298.

Not sure why it is E :S

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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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15 Nov 2011, 14:55
I also got A. Can we confirm?

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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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15 Nov 2011, 15:48
A for me as well. Any trick involved?
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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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25 Jan 2016, 05:28
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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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28 Jan 2016, 19:08
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64

Modify the original condition and the question. Since 298 buses are divided into three zones, it should be informed that how many t buses are in the blue zone, the red zone, and the green zone respectively. However, that information is in 1) & 2). Thus, the answer is E.
That is, in order to figure out variables, you need to know the number of q,r,s,t buses and t buses divided into each zone, which leads to a lot of variables. Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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29 Jan 2016, 09:12
Sorry for my language here but you could be please little bit more confusing. As of this, i was able to get tiny bit of information. **Sarcasm**

MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64

Modify the original condition and the question. Since 298 buses are divided into three zones, it should be informed that how many t buses are in the blue zone, the red zone, and the green zone respectively. However, that information is in 1) & 2). Thus, the answer is E.
That is, in order to figure out variables, you need to know the number of q,r,s,t buses and t buses divided into each zone, which leads to a lot of variables. Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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29 Jan 2016, 09:48
My answer is A but looks like the answer choice is E. Can you please explain. The first question does provide the ratio and the total of the buses in the garage with which we can solve the equation.

I think what I understand We can not assume t=rest buses, Then answer comes to E.

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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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30 Jan 2016, 07:16
I'd say it's E because it says "garageS" ... we don't know if those garages are outside the zones or located in one or different zones... confusing question with not enough details to answer it.

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Re: A certain city owns 298 buses, whose routes are divided into [#permalink]

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01 Feb 2016, 09:17
rxs0005 wrote:
A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64

Hi,

I have seen lot of discussion on this Q with few suggesting E as answer..

There has been a post claiming that we require so many equation as so many variables are there..
But the moment we have some ratios we can get down the number of equations required.
SO, lets be careful discarding choices

what info does the Q gives

there are 298 buses, whose vehicle are divided in three zones and few in garages..

lets see the statements now..

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.
since 26 buses are in garage, 298-26=272 are in three zones..
we are given the ratio of these three zones q:r:s=4:6:7..

this is clearly SUFFICIENT..
let the common ratio be x..
so the number of buses are..
4x+6x+7x=272..
x=272/17=16..
so q=4*16=64..
r= 6*16=96..
s= green zone= 16*7=102..
Sufficient

(2) q = 64..
just one zone..
clearly insuff..

ans A..

where the statement 2 helps us is that we have got q as 64 from statement 1 and the same has been reinforced in statement 2..

NOTE : IF ANY OTHER EXPERT HAS A DIFFERENT VIEW, AS MATH REVOLUTION HAS, IT CAN BE DISCUSSED AND LETS CHANGE THE OA ACCORDINGLY TO CLEAR THE CONFUSION STUDENTS ARE HAVING.
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A certain city owns 298 buses, whose routes are divided into [#permalink]

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01 Feb 2016, 09:29
chetan2u wrote:
rxs0005 wrote:
A certain city owns 298 buses, whose routes are divided into three zones. At a given time, if q buses are in the blue zone, r buses are in the red zone, s buses are in the green zone, and t buses are in garages, how many buses are in the green zone?

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.

(2) q = 64

Hi,

I have seen lot of discussion on this Q with few suggesting E as answer..

There has been a post claiming that we require so many equation as so many variables are there..
But the moment we have some ratios we can get down the number of equations required.
SO, lets be careful discarding choices

what info does the Q gives

there are 298 buses, whose vehicle are divided in three zones and few in garages..

lets see the statements now..

(1) The ratio of q to r to s is 4:6:7 and 26 buses are in garages.
since 26 buses are in garage, 298-26=272 are in three zones..
we are given the ratio of these three zones q:r:s=4:6:7..

this is clearly SUFFICIENT..
let the common ratio be x..
so the number of buses are..
4x+6x+7x=272..
x=272/17=16..
so q=4*16=64..
r= 6*16=96..
s= green zone= 16*7=102..
Sufficient

(2) q = 64..
just one zone..
clearly insuff..

ans A..

where the statement 2 helps us is that we have got q as 64 from statement 1 and the same has been reinforced in statement 2..

NOTE : IF ANY OTHER EXPERT HAS A DIFFERENT VIEW, AS MATH REVOLUTION HAS, IT CAN BE DISCUSSED AND LETS CHANGE THE OA ACCORDINGLY TO CLEAR THE CONFUSION STUDENTS ARE HAVING.

chetan2u, I think you are missing 1 thing from the discussions above. Firstly, the wording of the question is not GMAT standard. So will probably rate this question poor.

As for this discussion, you are assuming that none of those "garages" overlap with any one or more of the 3 zones. What if n number of those garages are in the blue zone. Thus out of the 26 buses in the garages, you do not know whether 4 or 6 or 10 or 14 are overlapping with the blue zone buses etc. This is the point of contention because of which the OA is E.

You are arriving at A by assuming that none of those garages overlap with the 3 zones, which is again a good assumption but not something that the question was allowing to be assumed.

This is the logic that MathRevolution has applied as well. There is no other way E can be the OA (yes, the OA per Kaplan is in fact E as mentioned by one of the posters above). We can spend many hours on discussing your or someone else's point of view but we will not be able to get to know from Kaplan whether there was a typo.

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A certain city owns 298 buses, whose routes are divided into   [#permalink] 01 Feb 2016, 09:29

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