Data Sufficiency

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

Official Guide question
Answer: C

Statement 1 alone appears to be sufficient to me. The question implies 2 equations: 15x = Gross Revenue in one week from oranges and 18g = Gross Revenue in one week from grapefruit. So, embedded in the question is a system of equations.

Then, from Statement 1 we learn that x = 2g + 20. Well, 15x = Revenue. So, I can solve for x in terms of g, right? Thus, 15 (2g + 20) = R; Thus, 30g + 300 = R. g = 10, g being the number of grapefruit.

I can put that number back into the equation denoting the relationship given in Statement 1 which was x = 2g + 20. Thus, x = 2(10) + 20 = x = 40. There are 40 crates of oranges that were shipped last week.

Statement 1 alone is sufficient.

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I really just want someone who understands what I'm missing to explain the answer. I wrote to Magoosh since I am paying them for their GMAT review and did not get an answer. Here is they're answer:

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-tric ... ns-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

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Michele Wells

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OK great! Now we are on the same page about what the question actually means

The next step is to consider the statements each in turn right. Let's do that. Enter statement 1 which reads:

"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, here I have an understanding of the relationship between two variables "x" and "g".

So, as I wrote before

"Then, from Statement 1 we learn that x = 2g + 20." Well, 15x = Revenue. So, I can solve for x in terms of g, right? Thus, 15 (2g + 20) = R; Thus, 30g + 300 = R. g = 10, g being the number of grapefruit.

I can put that number back into the equation denoting the relationship given in Statement 1 which was x = 2g + 20. Thus, x = 2(10) + 20; = x = 40. There are 40 crates of oranges that were shipped last week.
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Please help XX

Brent@GMATPrepNow wrote:

jjjinapinch wrote: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

Official Guide question
Answer: C

Target question: How many crates of oranges did the grower ship last week?
Let R = # of crates of oranges shipped last week
Let G = # of crates of grapefruit shipped last week

Our goal is to determine the value of R

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.
We can write: R = G + 20
There are infinitely many values of R and G that satisfy statement 1. Here are two:
Case a: R = 21 and G = 1, in which case 21 crates of oranges were shipped
Case b: R = 22 and G = 2, in which case 22 crates of oranges were shipped
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped
We can write: 15R + 18G = 38,700
There are MANY possible solutions to this equation.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that R = G + 20
Statement 2 tells us that 15R + 18G = 38,700
Since we COULD solve this system for R and G, we COULD determine the number of crates of oranges sold. Of course, we're not going to waste our time solving the system, since our sole objective is to determine whether we have sufficient information to answer the target question with certainty (which we do!)

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent