Peter went to the store to buy paint. Small cans cost $30 and larger

Question

Peter went to the store to buy paint. Small cans cost $30 and larger cans cost $80. How many small cans of paint did he buy?

(1) Peter spent $220 on paint.
(2) Peter bought four cans of paint in total.

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Some problems on the GMAT Quant section cannot be solved with formulas or with algebra. For some problems, the GMAT makes you wrestle with the number properties themselves. For a discussion of difficult numerical reasoning questions, as well as the full solution to this question, see:
https://magoosh.com/gmat/2013/difficult ... questions/

Mike

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Official Answer

A

Paris75 · Answer

Not really a 700 question but nevertheless an interesting one:

Choice A: If you buy one can at 80, than there are no way to reach the $220. If you buy zero also. And if you buy three than you are already at 240. Than you need two cans at $80 and two at $30. CORRECT

Choice B: no clear information

ANSWER A.

Hope it helps!

jlgdr · Answer

Not really a 700 question.
Not really a Number Property question, this should be tagged as a Word Problem

Integer constraints are commonly tested on the GMAT

This problem is meant to deal with exactly that

I suggest always simplifying first

3x + 8y = 22

And then x = 22 - 8y / 3

Only 2 works here

Cheers!
J

mikemcgarry · Answer

Dear jlgdr , By your statement " Only 2 works here ", do you mean statement #2? In other words, do you mean to imply that (B) is the answer? If not, it's not clear to me what you think the answer is. Furthermore, I would argue that introducing algebra into this problem doesn't necessarily facilitate the solution, and for some students, may confuse them. Mike :-)

chetan2u · Answer

Hi

Firstly I am sure this Q must have been discussed earlier too.

Let's see the statements..
I. It gives us equation 30s+80b=220...
ONLY possibility is s=b=2
Sufficient

II. 4 cans can be any combination..
All 4 big. All 4 small. 1&3 etc
Insufficient

A

Birla · Answer

(A) 
Statement 1 - total spending 220$ 
We know that number of cans will be a natural number.
Let x be number of small cans and y be number of large cans
If y=1 then 30x=140 => no solution 
If y=2 then 30x=60=> x=2 
Then y cannot be 3 otherwise sum will be greater than 220.
Statement 1 is sufficient.

Statement 2 : Total 4 cans 
Possible cases
(0,4)
(1,3)
(2,2)
(3,1)
(4,0)

Only statement 1 is sufficient 
(A)

adkikani · Answer

chetan2u

The moment I see two variables I immediately concluded that I need a second linear equation.
How to avoid this  trap ?

Bunuel · Answer

Generally such kind of linear equations (ax + by = c) have infinitely many solutions for x and y, and we cannot get single numerical values for the variables. But, here in 30x + 80y = 220, x and y must represent the # of cans, so they must be non-negative integers and in this case 30x + 80y = 220 is no longer simple linear equation, it's a Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there  might be  only one combination of x and y possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case.

For more, check  C-Trap Question Collection  from our  Special Questions's Directory .

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Peter went to the store to buy paint. Small cans cost $30 and larger

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