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).

The oa is E

thanks srinivasssrk, i fell for it.

Yup answer is E.

(1) and (2) are the same thing

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.

An interesting article at Karishma's (from Veritas) old blog to solve such equations:

http://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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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.

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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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

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.