Problem Solving

At a certain bakery, each rol costs r and each doughnut costs d cets. If Alfredo ought 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 wold have paid $10.0 if he had bought 16 rolls and 12 doughnuts.

OA is E

Hi Arbiter,

Firstly this is not a Problem solving question. Request you to post appropriate questions in the forum. Thanks.

Statement 1: Not sufficient because in terms of an equation, this is how it can be represented: 8r+6d=$5. Does not allow us to determine the values of r & d to answer the question.

Statement 2: Not sufficient because in terms of an equation, this is how it can be represented: 16r+12d=$10. Does not allow us to determine the values of r & d to answer the question.

Both statement combined will also not help, because both the statements are equivalent. Not sufficient.

Hence E. Hope this helps.

Typically when you have 2 equations with 2 unknowns you can solve for the answer.

In this case we have:

8R + 6D = 5
16R + 12D = 10

In actuality, these equations are the SAME, but scaled. (2) is just two times (1). In this case, we cannot solve for the unique (R,D) pair that satisfies the given information.

2 linear equations/2 unknowns will always give you an answer, unless the lines are equal.

Typically when you have 2 equations with 2 unknowns you can solve for the answer.

In this case we have:

8R + 6D = 5
16R + 12D = 10

In actuality, these equations are the SAME, but scaled. (2) is just two times (1). In this case, we cannot solve for the unique (R,D) pair that satisfies the given information.

2 linear equations/2 unknowns will always give you an answer, unless the lines are equal.

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

But in this case why isnt your logic working? OA is A.

Sorry for posting a question in the thread, but i had no other way of expressing my doubts than copying this question here in this thread.[/quote]

rb90 wrote:

Typically when you have 2 equations with 2 unknowns you can solve for the answer.

In this case we have:

8R + 6D = 5
16R + 12D = 10

In actuality, these equations are the SAME, but scaled. (2) is just two times (1). In this case, we cannot solve for the unique (R,D) pair that satisfies the given information.

2 linear equations/2 unknowns will always give you an answer, unless the lines are equal.

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

But in this case why isnt your logic working? OA is A.

Sorry for posting a question in the thread, but i had no other way of expressing my doubts than copying this question here in this thread.

Normally, when we have 2 variables, we look for 2 distinct linear equations in order to solve for each variable. However, when a problem is restricted to positive integers, sometimes 1 equation will be sufficient to solve for 2 variables.

In the DS question above, statement 1 tells us that 15x + 29y = 440. Because x and y represent the numbers of stamps being purchased, x and y must be positive integers. Only one set of positive integers works:
15(10) + 29(10) = 440. Thus, given only the 1 equation, we can determine that Joanna purchased 10 of each kind of stamp.

For a more detailed explanation, go here: https://www.beatthegmat.com/123-131-arit ... 61266.html

GMATGuruNY wrote: Normally, when we have 2 variables, we look for 2 distinct linear equations in order to solve for each variable. However, when a problem is restricted to positive integers, sometimes 1 equation will be sufficient to solve for 2 variables.

In the DS question above, statement 1 tells us that 15x + 29y = 440. Because x and y represent the numbers of stamps being purchased, x and y must be positive integers. Only one set of positive integers works:
15(10) + 29(10) = 440. Thus, given only the 1 equation, we can determine that Joanna purchased 10 of each kind of stamp.

For a more detailed explanation, go here: https://www.beatthegmat.com/123-131-arit ... 61266.html.

Hi Mitch, I've read a number of your explanations and they are all fantastic. Recently, I was having some difficulty with triple overlapping sets and your approach to focus on the "overlap" is the only one that made intuitive sense to me.

With regard to this question, is there a quick way to know if a particular two variable equation that is restricted to positive integers can be solved. In the stamp question, I would have picked C because I would have assumed that the two variable equation in statement 1) could not be solved. Picking numbers to test the sufficiency of an equation is time consuming. Is there any quicker way to do this? Thanks.

BTW the link isn't working.

rkanthilal wrote:

GMATGuruNY wrote: Normally, when we have 2 variables, we look for 2 distinct linear equations in order to solve for each variable. However, when a problem is restricted to positive integers, sometimes 1 equation will be sufficient to solve for 2 variables.

In the DS question above, statement 1 tells us that 15x + 29y = 440. Because x and y represent the numbers of stamps being purchased, x and y must be positive integers. Only one set of positive integers works:
15(10) + 29(10) = 440. Thus, given only the 1 equation, we can determine that Joanna purchased 10 of each kind of stamp.

For a more detailed explanation, go here: https://www.beatthegmat.com/123-131-arit ... 61266.html.

Hi Mitch, I've read a number of your explanations and they are all fantastic. Recently, I was having some difficulty with triple overlapping sets and your approach to focus on the "overlap" is the only one that made intuitive sense to me.

With regard to this question, is there a quick way to know if a particular two variable equation that is restricted to positive integers can be solved. In the stamp question, I would have picked C because I would have assumed that the two variable equation in statement 1) could not be solved. Picking numbers to test the sufficiency of an equation is time consuming. Is there any quicker way to do this? Thanks.

BTW the link isn't working.

Glad to know that you've been finding my posts helpful. Thanks for the kind words. I fixed the link in my post above; please feel free to retry it.

When a DS question with two variables and one equation is restricted to positive integers, we should err on the side of caution and verify that more than one solution is possible. We should be especially wary when:

-- the problem includes additional restrictions
-- the problem involves a strange combination of numbers (15, 29 and 440 are not easy numbers to combine)

I personally find it easiest just to look at the numbers and at the restrictions and to try out different scenarios. I know that if only one set of solutions is possible, I won't have to try too many options, because the problem will be quite restricted. Please feel free to check the link to the stamps problem to see how I streamlined the process.