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# 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 cups of pasta that Malik will use the next time he prepares this dish? GMAT Explanation

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 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.

## Define the question: What is the number of cups of pasta that Malik will use the next time he prepares this dish?

One key thing to note here is that we need the number of cups for the next time he prepares this dish. Just because the recipe is for 4 servings does not necessarily mean Malik will be making that amount of food.

So, we need to be looking out for information on how many servings Malik is planning on making.

## Organize the information: What does the recipe tell us?

The recipe says that 4 servings of the dish require 3/2 cups of pasta. Let’s think about this using proportions, since recipes are proportional.

If Malik wanted to make 8 servings instead of 4, he would need 8/4 = 2 times the amount of pasta the recipe calls for, or 3/2 * 2 = 3 cups of pasta.

Let’s call ‘s’ the number of servings of the dish, and ‘p’ the number of cups of pasta needed to make that amount. We can write out the proportions mathematically as:

$\frac{s}{4 \text{ servings}} = \frac{p}{\frac{3}{2} \text{ cups of pasta}}$

We can cross multiply to get a simpler equation (and also drop the units for clarity):

$4p = \frac{3}{2}s$

With this relationship in mind, let’s take a look at statement 1.

## (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.

Since we don’t know how many servings Malik made the last time, we still don’t know how many servings he will make the next time. So statement 1 is insufficient.

Let’s try the next statement.

## (2) Malik used 6 cups of pasta the last time he prepared this dish.

With this information, we can use the equation from our proportions before to find the number of serving Malik made the last time.

$4*6 = \frac{3}{2}s$

$24 = \frac{3}{2}s$

$24*\frac{2}{3} = s$

$s = 16$

Great! Now we know Malik prepared 16 servings of the dish last time. But, we still don’t know how many servings Malik is planning on preparing next time.

Insufficient.

## Let’s try both statements together:

Well, we know Malik made 16 servings last time from statement 2. We also know that the next time, Malik will make half as many servings as he did last time.

This means next time, Malik is planning on making 16/2 = 8 servings next time.

Since we have proportions relating servings to cups of pasta, we know we can find the number of cups of pasta Malik will need next time. So, we have all the information we need. Still, let’s finish off the question to make sure.

Plugging in 8 for the number of servings into our proportions equation, we have:

$4p = \frac{3}{2}*8$

$4p = 12$

$p = 3$

So, we know Malik will need 3 cups of pasta the next time he makes the dish. Both statements together were sufficient.