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At a certain bakery, each roll costs r cents and each doughnut costs

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joemama142000
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At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   18 Dec 2005, 18:08
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At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

(1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts
(2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts
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E
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srinivasssrk
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   18 Dec 2005, 18:11
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This is a typical GMAT trap. YOu might have seen my earlier post about picking numbers for DS. In general, two equations in two unknowns can be solved to get a unique (one) solution except when the two equations are the same. If you divide the information in statement 2, you get statemetn 1. So, statemetn 2 is not giving you any new information. Hence, the answer should be E.

-Srinivas (mathguru).
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joemama142000
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   18 Dec 2005, 19:28
The oa is E

thanks srinivasssrk, i fell for it.
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   18 Dec 2005, 20:28
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Yup answer is E.

(1) and (2) are the same thing
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strange
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   18 Dec 2005, 20:35
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TeHCM wrote:
Yup answer is E.

(1) and (2) are the same thing


For once, I get the right answer.. :-D
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   19 Dec 2005, 01:51
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joemama142000 wrote:
At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts

2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts


From stmt1 we get 8r+6d = 5
From stmt2 we get 16r + 12d = 10

Stmt1 * 2 = stmt 2, and we will not be able to solve this equen. So my answer is E.
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Re: Marta bought several pencils. if each pencil was either 23 [#permalink] New post   13 Nov 2011, 03:35
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An interesting article at Karishma's (from Veritas) old blog to solve such equations:

https://gmatquant.blogspot.com/search?up ... -results=7

Hope it will help someone as it helped me :)
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   05 Jan 2015, 04:12
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At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

Let \(r\) be the price of rolls in cents and \(d\) be the price of doughnuts in cents. Note that \(r\) and \(d\) must be an integers. Q: \(r=?\)

(1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts --> \(8r+6d=500\) --> \(4r+3d=250\). Multiple solutions are possible, for instance: \(r=25\) and \(d=50\) OR \(r=10\) and \(d=70\). Not sufficient.

(2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts --> \(16r+12d=1000\) --> \(4r+3d=250\). The same. Not sufficient.

(1)+(2) No new info. Not sufficient.

Answer: E.

Check similar questions here: c-trap-questions-177044.html
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   06 Sep 2016, 23:44
Statement 1: 8r+6d=500 (Dollars to cents). Multiple values of r & d can work. For ex: r=10,d=70 & r=40, d=30. Not sufficient.
Statement 2: This is a tautological statement. (As St:1 is multiplied by 2).

Hence, option E.
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   08 Feb 2017, 21:26
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cost of each roll=r cents
cost of each doughnut=d cents

statement 1:

8r+6d=500

We have only one equation and 2 unknowns

Insufficient

statement 2:

16r+12d=1000
8r+6d=500( dividing by 2 throughout)

This is nothing but the same equation in statement 1..

Insufficient

Combining both the statements we have a single equation 8r+6d=500
and 2 unknowns...Hence the value of r cannot be determined

The ans is clearly E.
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   13 Feb 2017, 12:02
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Experts, is there a FAST way to detect if we are dealing with that situation (I don't remember the name) when we have 2 variables and it seems INSUF, but them there is only one combo of numbers that makes the equation possible, so it is SUF? How can we quickly check if that is the case? Here I was indecisive between D and E.
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   14 Jun 2020, 07:47
iliavko wrote:
Experts, is there a FAST way to detect if we are dealing with that situation (I don't remember the name) when we have 2 variables and it seems INSUF, but them there is only one combo of numbers that makes the equation possible, so it is SUF? How can we quickly check if that is the case? Here I was indecisive between D and E.


Hi, this may help link
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   26 Dec 2020, 07:21
At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

Stat1: Alfredo paid $5.00 for 8 rolls and 6 doughnuts
It means, 8*r + 6*d = 500, or, 4*r + 3*d = 250, now, 4*r = 160 or 40 and 3*d= 90 or 210 respectively. Not sufficient.
Stat2: Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts
It means, 16*r + 12*d = 1000, or, 4*r + 3*d = 250. It is same like statement 1. Not sufficient.

Combining 1 and 2, Still we have 1 equation and 2 probable value of r. Not sufficient.

So, I think E. :)
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   30 Nov 2021, 08:27
Bunuel wrote:
At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

Let \(r\) be the price of rolls in cents and \(d\) be the price of doughnuts in cents. Note that \(r\) and \(d\) must be an integers. Q: \(r=?\)

(1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts --> \(8r+6d=500\) --> \(4r+3d=250\). Multiple solutions are possible, for instance: \(r=25\) and \(d=50\) OR \(r=10\) and \(d=70\). Not sufficient.

(2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts --> \(16r+12d=1000\) --> \(4r+3d=250\). The same. Not sufficient.

(1)+(2) No new info. Not sufficient.

Answer: E.

Check similar questions here: https://gmatclub.com/forum/c-trap-questions-177044.html


Bunuel GMATNinja (1) How did you come up with these solutions? (2) How to come up with solutions quickly? I'm taking too much time doing try & error...tks!
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   08 Feb 2022, 08:17
Bunuel Is there a fast way / formula to check if multiple solutions exist??? I know once you find the first solution, you can take the solution and add/subtract by the other number's multiplier to get additional solutions and check if they are in range. But what is the fastest way to either 1) get that first solution so that you can check if there are more, or 2) see there are multiple solutions possible? This seems to take more than 2 min
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   16 Feb 2022, 03:13
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testtakerstrategy wrote:
Bunuel Is there a fast way / formula to check if multiple solutions exist??? I know once you find the first solution, you can take the solution and add/subtract by the other number's multiplier to get additional solutions and check if they are in range. But what is the fastest way to either 1) get that first solution so that you can check if there are more, or 2) see there are multiple solutions possible? This seems to take more than 2 min


Not sure if I understood your query~, but I will say this!
For this kind of DS problem, you do not have to really solve it to know the answer. The first statement is giving you an equation which is like 8x+6y =5
Not sufficient as we do not have integer constraints for the price of the roll or doughnut.

Similarly . for second statement , the equation will be 16x + 12y = 10. Insufficient because of the same logic used in Statement 1.
Combining it,

If you observe the two equations are identical because if you multiply the first equation by 2, you will get the second statement's equation. Hence no additional information to solve. Hence answer is E
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   06 Aug 2023, 02:48
This is a trap question. Both the equations are the same. Hence E

Although, don't choose E right away upon encountering two equations that are the same. Try to put values, if that equation has a unique solution then D would be your answer, and not C (that's another trap).

But here, we don't have a unique solution, hence choose E
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   05 Jan 2024, 13:45
Bunuel wrote:
At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

Let \(r\) be the price of rolls in cents and \(d\) be the price of doughnuts in cents. Note that \(r\) and \(d\) must be an integers. Q: \(r=?\)

(1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts --> \(8r+6d=500\) --> \(4r+3d=250\). Multiple solutions are possible, for instance: \(r=25\) and \(d=50\) OR \(r=10\) and \(d=70\). Not sufficient.

(2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts --> \(16r+12d=1000\) --> \(4r+3d=250\). The same. Not sufficient.

(1)+(2) No new info. Not sufficient.

Answer: E.

Check similar questions here: https://gmatclub.com/forum/c-trap-questions-177044.html


Hi Bunuel, in a DS question if (1) and (2) provide the same information can we directly assume that the answer is E? Or are there any instances where it is C? Thank you for your reply !
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Re: At a certain bakery, each roll costs r cents and each doughnut costs [#permalink] New post   05 Jan 2024, 14:00
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chloe2m wrote:
Bunuel wrote:
At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll?

Let \(r\) be the price of rolls in cents and \(d\) be the price of doughnuts in cents. Note that \(r\) and \(d\) must be an integers. Q: \(r=?\)

(1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts --> \(8r+6d=500\) --> \(4r+3d=250\). Multiple solutions are possible, for instance: \(r=25\) and \(d=50\) OR \(r=10\) and \(d=70\). Not sufficient.

(2) Alfredo would have paid $ 10.00 if he had bought 16 rolls and 12 doughnuts --> \(16r+12d=1000\) --> \(4r+3d=250\). The same. Not sufficient.

(1)+(2) No new info. Not sufficient.

Answer: E.

Check similar questions here: https://gmatclub.com/forum/c-trap-questions-177044.html


Hi Bunuel, in a DS question if (1) and (2) provide the same information can we directly assume that the answer is E? Or are there any instances where it is C? Thank you for your reply !


If two statements in a data sufficiency question provide the same information, and this information is individually insufficient, then obviously, combining them won't yield any new insights. Thus, even when taken together, these statements would not be sufficient.
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