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

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).

Yup answer is E.

(1) and (2) are the same thing

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

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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For once, I get the right answer..

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.

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.

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.

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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The oa is E

thanks srinivasssrk, i fell for it.

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.

Hi, this may help link

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.

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!

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

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

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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