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# Peter went to the store to buy paint. Small cans cost \$30

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486
Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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19 Dec 2013, 10:03
3
7
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:28) correct 31% (01:23) wrong based on 348 sessions

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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?
Statement #1: Peter spent \$220 on paint.
Statement #2: Peter bought four cans of paint in total.

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:
http://magoosh.com/gmat/2013/difficult- ... questions/

Mike

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Mike McGarry
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Re: Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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23 Dec 2013, 14:45
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

Hope it helps!
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Re: Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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07 Jan 2014, 09:09
mikemcgarry wrote:
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?
Statement #1: Peter spent \$220 on paint.
Statement #2: Peter bought four cans of paint in total.

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:
http://magoosh.com/gmat/2013/difficult- ... questions/

Mike

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
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486
Re: Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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07 Jan 2014, 10:13
1
jlgdr wrote:
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

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
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Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Posts: 7334
Re: Peter went to the store to buy paint. Small cans cost \$30 and larger  [#permalink]

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19 Apr 2017, 18:42
anupam87 wrote:
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?

Statement #1: Peter spent \$220 on paint.

Statement #2: Peter bought four cans of paint in total.

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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Peter went to the store to buy paint. Small cans cost \$30 and larger  [#permalink]

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19 Apr 2017, 18:57
(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)
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Re: Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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14 Dec 2017, 17:41
chetan2u

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

The moment I see two variables I immediately concluded that I need a second linear equation.
How to avoid this trap?
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Posts: 53063
Re: Peter went to the store to buy paint. Small cans cost \$30  [#permalink]

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14 Dec 2017, 19:52
chetan2u

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

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

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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Re: Peter went to the store to buy paint. Small cans cost \$30   [#permalink] 14 Dec 2017, 19:52
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