Malik’s recipe for 4 servings of a certain dish requires 3/2

[rschunti]

Malik’s recipe for 4 servings of a certain dish requires 3/2 cups of pasta. According to this recipe, what is the number of the cups of pasta that Malik will use the next time he prepares this dish?
(1) The next time he prepares this dish, Malik will make half as many servings as he did the last time he prepared the dish.
(2)Malik used 6 cups of pasta the last time he prepared this dish.

This is GMATPREP question. What is the best approach to solve this question?

[RonPurewal]

(1)
no quantitative information at all.
for all we know, malik could have fed the entire 101st airborne last time. likewise, he might have made just 1 serving (or even 0.00001 serving).
insufficient

(2)
no information at all about this time.
insufficient

(together)
if you want, you could actually solve proportions to figure out how many servings malik made last time, then halve that, then transform back to cups of pasta. but ... why would you want to do that?
since recipes use direct proportions, statement (1) tells us that malik will require exactly half as many cups of pasta as last time. therefore, using statement (2), we can figure out that he'll need 3 cups of pasta.

answer = c

[mgmat.cr]

"Malik’s recipe for 4 servings of a certain dish requires 3/2 cups of pasta."

Does not this piece of information implicitly states that for 4 servings, total 6 cups of pasta were required.

And this statement 1 is sufficient to solve this problem.

But OA suggest C. So it seems like we are not supposed to assume anything at all unless it is explicitly stated.

I request the Instructors to suggest how to approach the problem statements.

[mschwrtz]

No, the info in the question does not imply that Malik made 4 servings last time. It just gives a ratio, pasta:servings=3/2:4.

People often draw similarly spurious conclusions about rates. "Train X travels at a constant rate of 130 kilometers in 1 hour" gives us just a rate; it doesn't tell us anything about the actual time or distance, outside of their relationship.

By the way, notice that your interpretation of the question contradicts S2. That means that your interpretation is wrong.

[gmat_professor]

The question requires 3 assumptions:
1) All the 4 receipes are of the same size.
2) All contain uniform quantity of Pasta.
3) Everytime Malik makes new receipes they are of the same size as the previous ones.

I have seen in many questions, especially involving sets, that such assumptions are tken into consideration.

One must also not forget that this is a question involving DS.

[jnelson0612]

The question requires 3 assumptions:
1) All the 4 receipes are of the same size.
2) All contain uniform quantity of Pasta.
3) Everytime Malik makes new receipes they are of the same size as the previous ones.

I have seen in many questions, especially involving sets, that such assumptions are tken into consideration.

One must also not forget that this is a question involving DS.

1) If you mean "servings", then yes, we should use the common sense approach of assuming that one serving is the same size as another serving of the same dish. A "serving" itself is a unit and in this case we know that the recipe produces four roughly equal servings.
2) I don't think you have to assume this--if one serving contains one more noodle than another serving, so be it. We know that 3/2 cups of pasta does produce four servings.
3) Not sure what you mean here. The problem clearly shows us that Malik can vary the amount of food he makes by increasing the recipe.

Thank you,

[rachelhong2012]

I was also stumped by this question and took around 3 minutes to solve it. I feel pretty uncomfortable when it comes to word translation problem because setting up the equation itself takes more than 1 minute and solving for variables (not entirely but at least partially to get close enough to what I want) takes another 1 minute or so.

So I began to approach those problems from the standpoint of thinking about the relationship between existing variables.

If I have two variables multiply by each other in an equation (SUCH AS IN RTD, work problem etc.) and I don't know what their product yields to, then what information can help me solve for both of them?

1. There must be a piece of information that gives me the constant, or hard number, of the product of these two variables

2. I have to be able to solve the equation in terms of one variable and one constant, so either:

Another piece of information tells me the relationship between these two variables so I can write two variables in terms of one variable.

OR the information gives me the constant for one of the two variables, so I still end up with only one variable to solve in the equation.

The rule of thumb is:

One variable, one constant, one equation, and you'll be to crack the equation (assuming it's not a quadratic equation which can yield to both postive and negative results, but in the case of word translation, this is no longer an issue since result is 99% positive).

Going back to this problem specifically, you see a ratio.

I treat ratio problem like this:

It tells me the relationship between two variables, so if I have to solve for one of them, I need the hard number, or constant for the other one.

In this problem, I express ratio in such way:

This time serving : This time cups (?)
In other words, This time serving (?)
IF I have the hard number for This time serving, using their relationship (direct proportion), I can solve for This time cups

**note since I'm revisiting the problem, I know I have to make the distinction of "this time"

statement 1: This time serving : last time serving
Great, no hard number for This time serving, rather, another ratio. Now instead of worrying about This time serving, I have to think about how to find the hard number for last time serving

IF x: y and y: z, THEN X: Z
If x is directly related to y and y is directly related to z, then x is directly related to z. Meaning if I get a hard number for x, I can solve for z, vice versa.

Here the new ratio becomes:

This time serving : This time cups (?)
This time serving : Last time serving
OR This time cups (?) : Last time serving

statement 1 is insufficient

Let's look at statement 2:

Given the hard number for Last time cups
we now know that last time cups : last time servings because the ratio between serving and cups is already preset, is always true.
Which means we now have:

Last time cups : Last time servings
don't know how this relates to this time servings and cups, in succicient.

However, combine both statements:

This time cups (?) : Last time serving
Last time cups : Last time servings

Or This time cups (?) : Last time cups
Since we're given the hard number for last time cups, we can find this time cups, so C.


This is a very convoluted ratio problem, that's why my explanation is also damn long, but if you use this theoretical approach and apply it to other similar problems, you can crack those problems more quickly.

Cheers :)

[jnelson0612]

Wow rachel, I love the amount of time and thought you have put into this! Thanks for posting!