Quantity * Price Data Sufficiency

[THANU.KG]

Hi,
Since I cannot post problems from the OG, I thought I could rephrase the question. I cannot understand how and why there is no whole number constraint (since crates can only be a whole number) on this and why C would be the answer. I was thinking only B was sufficient.

A farmer receives $15 for each crate of potatoes shipped and $18 for each crate of tomatoes shipped. How many crates of potatoes did the farmer ship last week?

(1). Last week the number of crates of potatoes that farmer shipped was 20 more than twice the number of crates of tomatoes shipped.
(2). Last week the farmer received a total of $38,700 from the crates of potatoes and tomatoes shipped.

In the example above, the second statement gives us
15P+18T=38,700

Why can we not start plugging in numbers for P and T to find out what the number would be since they can be only whole numbers? Please help.

[tim]

well, what happened when you started plugging in numbers? did you get exactly one possibility?

[THANU.KG]

Hi Tim,

I started plugging in numbers after you asked me this question. I am able to get a whole number for P=0; T=2150 AND when T=800;P=1620 (this obviously i got ONLY when i solved both the equations).

I agree that this alone is enough to prove that C should be the answer choice. But we have seen similar questions where one equation was sufficient. How can I figure it out here? Obviously I cannot be plugging in numbers that go beyond a certain number, 800 in this case.

Please help.
Thanks

[RonPurewal]

Hi Tim,

I started plugging in numbers after you asked me this question. I am able to get a whole number for P=0; T=2150 AND when T=800;P=1620 (this obviously i got ONLY when i solved both the equations).

I agree that this alone is enough to prove that C should be the answer choice. But we have seen similar questions where one equation was sufficient. How can I figure it out here? Obviously I cannot be plugging in numbers that go beyond a certain number, 800 in this case.

Please help.
Thanks

in this problem, it should be plain that you're going to have lots and lots of possibilities, because you're talking about hundreds or even thousands of crates, each priced at $15 or $18.
the deal is this: if you have the expression 15x + 18y, then you can "trade" eighteen x's for fifteen y's and get the same sum. if the values of x and y are well into the hundreds or thousands, then you're going to have plenty of chances to make such "trades", so you'll get multiple answers.

if the values of x and y were substantially smaller -- to the point where they created any shadow of a doubt -- then you'd have to start testing cases.