Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #4

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# A citrus fruit grower receives \$15 for

A citrus fruit grower receives \$15 for crate of oranges shipped and \$18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

### 2 Explanations

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NIKHIL BORKER

Reacting to Mike's solution : To take for granted that because we have an equation 15A+18B=38700,no unique solution exists is wrong.

Let's say we were given that the total revenue from the fruits shipped is \$63, then that would have automatically implied that 3 crates of oranges and 1 crate of grapefruit was sold. It is important to note that we have an integer constraint (crates cannot be fractions!) here

The LCM of 18 and 15 is 90 and the given revenue is a lot greater than \$90. So, we can always replace 5 crates of grapefruit with 6 crates of oranges.

For example, we could have 38700/15=2580 crates of oranges or 2574 crates of oranges and 5 crates of grapefruit and so on.....
Hence, no unique solution exists

Please correct me if my concern above is unfounded

Jan 23, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Nikhil,

Good point :) Since we have an integer constraint in this problem, it could be the case that we could answer the question by using the information provided in the question and the equation from Statement 2. However, and as you shown, even considering the integer constraint, there is more than one possible combination of orange and grapefruit crates given the information in Statement 2. So, the statement alone is insufficient.

Feb 6, 2016 • Reply

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Mike McGarry, Magoosh Tutor

Aug 17, 2015 • Comment