Last Updated on May 5, 2023
GMAT OFFICIAL GUIDE DS
We are given that a citrus grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. We can define some variables for the number of crates of oranges shipped and the number of crates of grapefruit shipped.
Let R = the number of crates of oranges shipped and G = the number of crates of grapefruit shipped.
We need to determine the value of R.
Statement One Alone:
Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.
Using statement one we can set up the following equation:
R = 20 + 2G
We cannot determine the value of R, so statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.
From statement two we can set up the following equation:
15R + 18G = 38,700
We cannot determine the value of R, so statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two we have the following equations:
1) R = 20 + 2G
2) 15R + 18G = 38,700
We can simplify the second equation by dividing the entire equation by 3:
3) 5R + 6G = 12,900
At this point we substitute (20 + 2G) from equation (1) for R in equation (3), giving us:
5(20 + 2G) + 6G = 12,900
Now, at this point, we know we can determine a value for G and thus determine a value for R. If we were taking the actual test, we could stop at this point and say that the answer is C. However, let’s finish the math to show the steps in evaluating R.
100 + 10G + 6G = 12,900
100 + 16G = 12,900
G = 12,800/16
G = 800
Since R = 20 + 2G, R = 20 + 2(800) = 1,620.
Answer: C
