Source: Official Guide for the GMAT 12th Ed. Section 6.3 Data Sufficiency; #8

1

A citrus fruit grower receives $15 for each

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week? (1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped. (2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

3 Explanations

1

Michele Wells

Deleted

May 29, 2018 • Comment

Sam Kinsman, Magoosh Tutor

Hi Michele,

Yes, you are right about the following two equations:

15x = Gross Revenue in one week from oranges
18g = Gross Revenue in one week from grapefruit

However, this doesn't give us enough information to answer the question. Let me explain why that is!

To keep things simple, let's use Rx to refer to revenue from oranges, and Rg to refer to revenue from grapefruit. So we have the following 3 equations:

15x = Rx
18g = Rg
x = 2g + 20

Here, we have 3 equations, and four different variables (also called "unknowns"): x, g, Rx, and Rg.

Whenever we have a system of equations, and we have more unknowns than equations, we don't have enough information to solve the system of equations. This is explained in this blog post: https://magoosh.com/gmat/2015/gmat-tricks-with-systems-of-equations-part-1/

So for this question, since we have more unknowns (4) than equations (3), we are stuck, and cannot solve for any of the variables.

May 29, 2018 • Reply

1

Michele Wells

Deleted

May 29, 2018 • Comment

Sam Kinsman, Magoosh Tutor

Hi Michele,

Happy to help! Let's take another look at Statement 1:

"Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped."

So we are told that the number of oranges shipped (we'll call that x) is 20 more than twice the number of grapefruits shipped (we'll call that g).

Using these variables, your equation is correct:

x = 2g + 20

However, we can't really say anything about the revenue at this point. We know that the farmer gets $15 per crate of oranges, and and $18 per crate of grapefruit. So we know that the revenue from oranges will be x*15, and the revenue from grapefruits will be g*18.

However, we cannot say that x*15 = revenue. You have to be careful here! x*15 = revenue from oranges, but not revenue from grapefruits.

Here, we cannot make any further equations. We could take:

x*15 = revenue from oranges

And plug in x = 2g + 20, to get

(2g + 20) * 15 = revenue from oranges

But this won't help us, because we don't what the revenue from oranges has to be equal to.

I hope this clarifies! :)

Best,
Sam

May 29, 2018 • Reply

1

Gravatar Mike McGarry, Magoosh Tutor

Nov 11, 2012 • Comment

Vasily Yakimenko

Is there a way to access these problems or the prompt? I have a hard time following the question description. Thanks!

Apr 4, 2019 • Reply

Adam Lyons, Magoosh Tutor

The full text of the problem should be visible here. Since these are official problems, though, you can find them on other sites through Google as well. I just copy and paste the first sentence in quotes and several websites pop up with the full text. Hope that helps!

Apr 5, 2019 • Reply

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Section 6.3 Data Sufficiency

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