What is the greatest number of markers that can be purchased for $18?

Question

(1) 4 markers or 6 pens or 12 pencils can be purchased for $36

(2) If the cost of each marker is increased by $3, 5 less markers can be purchased for $180

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GMATinsight · Answer

Question : Maximum markers that can be purchased in $18 = ?

STatement 1 : 4 markers or 6 pens or 12 pencils can be purchased for $36

4 markers = 6 pen = 12 pencils = $36

ie.. for $18 onecan buy only 2 markers

SUFFICIENT

STatement 2 : If the cost of each marker is increased by $3, 5 less markers can be purchased for $180

Let, cost of marker = c
and number of markers bought in $180 = x

180 = c*x

Also, 180 = (c+3)*(x-5)

i.e. c = 9 and x = 20

i.e. in $180, number of markers = 180/9 = 20

SUFFICIENT

Answer: Option D

Codebug4it · Answer

Answer:  Option D

Statement 1: 4 markers or 6 pens or 12 pencils can be purchased for $36

4 markers sold for 36$
 =>  2 markers = 36 / 2 = 18$

So, 2 markers can be sold for 18$

SUFFICIENT

Statement 2: If the cost of each marker is increased by $3, 5 less markers can be purchased for $180

(price of one marker) * (Num of markers) = 180$

After cost increased by 3$ each,

(price of one marker + 3) * (Num of markers - 5) = 180$

By solving above we can get:

=>  price of one marker = 9$
 =>  Num of markers = 20

So, 18$ / 9$ = 2 (2 markers can be sold for 18$)

SUFFICIENT

sachin91 · Answer

Statement 1:
In $36,4 markers can be purchased.
In $18,2 markers can be bought.
Hence,Statement 1 alone is sufficient.

Statement2:
Let total no of markers be x and price of each markers be y.
Intially,xy = 180 ----- eqn 1

After price is increased.
(x-5)(y+3) = 180. -- eqn 2

Since,we have two equations with two variables, we will get unique values of x and y.

Once,we find price of each market,which is y,we can find out numbet of markers that can bought for $18.
Hence,statement 2 alone is also sufficient.

Note: Don't waste time finding x and y as it is not required.

OA - D

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mayankmsr · Answer

Can anyone please explain why Statement 2 alone is sufficient?

As we have two variables, we will need value of atleast one variable to determine the exact value of other.

Considering, trial and error method, if we put random nos. of markers, we will get different values for the cost.

CrackverbalGMAT · Answer

From statement I alone, 4 markers can be purchased for $36. Therefore, cost of one marker = $9.
Greatest number of markers that can be purchased for $18 = 2

Statement I alone is sufficient. Answer options B, C and E can be eliminated.

From statement II alone, if the cost of each marker is increased by $3, 5 less markers can be purchased for $180.
If the cost of one marker is $x, number of markers =  \frac{180 }{ x} .

If the cost of one marker is $(x+3), number of markers =  \frac{180 }{ (x+3)}

The number of markers in the second case is 5 less than the number of markers in the first case.
Therefore, ( \frac{180}{x} ) – 5 = ( \frac{180}{x+3} ).

We have one equation in x, therefore, a definite value of x can be calculated. Since we can find a unique value for x, we can also find a unique value for the greatest number of markers that can be purchased for $18.

Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
Aravind B T

adityaganjoo · Answer

Bunuel  In Statement 2, can we assume that $180 is the exact amount required to pay for markers? What I mean to state is that there shall be no remainder when 180 is divided by the price of one marker?

Bambi2021 · Answer

I think this is a  poor quality question  and I dont agree with the OA.

(1) is clearly insufficient. It only states that 4 markers can be purchased for 36 dollars. It does not state whether 4 markers is the maximum number of markers that can be purchased for 36 dollars.

Maybe 6 markers can also be purchased for 36 dollars?

Either this is not an OG-question, or something must be missing in the transcription.

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Karan911 · Answer

Hi  chetan2u ,

So was trying to understand if we should at least form the quadratic and check if it leads to one positive root and one negative root in the 2nd statement?
Or just call it sufficient becasue we have 2 equations and 2 variables? What if we get 2 positive roots?

KabxW · Answer

Hey  Bunuel   bb   GMATNinja  
I want you to clarify please this question.
In statement A it gives that 4 markers can be purchased $36. It nowhere states that these markers are of the same price and hence we can't assume that 2 is maximum for $18
What if the price is $1, $1, $1 and $33. The the maximum will be 3 and not 2 (as stated in OA)

Please check this and tell me if this is even slightly close to an actual question.

bb · Answer

You are correct. The question does not state a number of assumptions. BUT, You have to assume that they are of the same price…. otherwise you would not be able to answer most questions on the GMAT. Imagine the question about a probability of picking a marble out of a box. E.g. you would not assume that marbles are different and one is the size of a P and another one is the size of an orange?

There are other potential issues with the question however.

Posted from my mobile device

bb · Answer

I spotted the same issue as well. The question does not say specifically if the price means exact amount or if you have money left over.

I am trying to figure out if that plays into the question and impacts the solution.

I’m also manually searching through my OG 11 and so far I’m not finding this question so you may be onto something here. It may not have been tagged correctly.

What is the greatest number of markers that can be purchased for $18?

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