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A citrus fruit grower receives $15

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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A citrus fruit grower receives $15

Post Mon Jul 24, 2017 9:25 am
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

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Top Reply
Post Mon Jul 24, 2017 10:06 pm
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
We have to find out how many crates of oranges did the grower ship last week.

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.

Say the number of crates of oranges that the grower shipped = x, and

the number of crates of grapefruit that the grower shipped = y

Thus, we have x = y + 20% of y = 1.2y

x = 1.2y. We do not have the value of y, thus, we cannot get the value of x. Insufficient.

Statement 2: Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped

=> x + y = 38700. We do not have the value of y, thus, we cannot get the value of x. Insufficient.

Statement 1 and 2:

From (2), we have x + y = 38700 and from (1), we have x = 1.2y

Since both the equations are unique and linear, we will get the unique value of x; there is no need to calculate its value. Sufficient.

The correct answer: C

Hope this helps!

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Post Mon Jul 24, 2017 9:56 am
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

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