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An 18 pages long book comprises either of 3 pages or 4 pages long chap : Quantitative Comparison Questions

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Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
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It is given that an 18 pages long book comprises either of 3 pages or 4 pages long
chapters.
We have to compare
Quantity A: The number of chapters with 3 pages
Quantity B: The number of chapters with 4 pages
Let us assume that the number 3 pages and 4 pages chapters in the book is 𝑥 and 𝑦
respectively.
Then we have, 3𝑥 + 4𝑦 = 18
Taking 𝑥 in terms of 𝑦, we get

x=18-4y/3 (equation 1)

Since, the number of pages cannot be in decimals or fractions so we need to find an
integer solution for eqn.1
Also, we can see that 18 – 4𝑦 should be a multiple of 3 to give integer value for 𝑥.
So, let us put value for 𝑦 and check if we are getting a positive integer for 𝑥.

If y=1, x=14/3 which is not an integer value.

Similarly, if 𝑦 = 2, 𝑥 = 10/3 which is not an integer value.

If y=3 x=6/3=2

which is an integer value.
So, we can see that 𝑥 = 2, 𝑦 = 3 is an integer solution for eqn.1
Now, if we take 𝑦 = 4 x=2/3 which is not an integer.
If we take 𝑦 > 4 then we will get 𝑥 < 0 which can’t be true.
Hence, the only integer solution we are getting for eqn.1 is 𝑥 = 2 and 𝑦 = 3.
So, Quantity A is 2 and Quantity B is 3.
Clearly, Quantity B is greater.
Ans. B
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Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
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ShowYoMoves wrote:
Can't there be only 3 page long chapters? Should the wording of the question clarify that both chapters of length 3 pages and 4 pages exist? Or is that to be assumed?

thats what i thought and the answer came out to be D
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Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
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nobefab410 wrote:
ShowYoMoves wrote:
Can't there be only 3 page long chapters? Should the wording of the question clarify that both chapters of length 3 pages and 4 pages exist? Or is that to be assumed?

thats what i thought and the answer came out to be D


Let's analyze the scenarios where there can be either 0 chapters with 3 pages or 0 chapters with 4 pages.

If there are 0 chapters with 3 pages:
x=0
x=0, and the equation becomes
4y=18
4y=18, which doesn't have a positive integer solution for y

If there are 0 chapters with 4 pages:
y=0
y=0, and the equation becomes
3x=18
3x=18, which doesn't have a positive integer solution for x.
In both cases, if one of the quantities is 0, the other quantity doesn't yield a positive integer solution. Therefore, both cases are not valid solutions

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Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
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Not sure if this is the correct methodology:

I think the question is asking if a book has BOTH 3 page chapters and 4 page chapters. If this is the case. 3x + 4y = 18.
Usually, you can't figure out two variables from one equation, but if there is an integer constraint, there's a math principle where all of the variables need to be multiples. For example 18 is a multiple of 3, so 4y has to be a multiple of 3. Out of 4, 8, 12, and 16, only 12 is a multiple of 3, so 4y = 12. y = 3 and x = 2. From here y > x, meaning B is the correct answer.
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Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
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Jakelong wrote:
nobefab410 wrote:
ShowYoMoves wrote:
Can't there be only 3 page long chapters? Should the wording of the question clarify that both chapters of length 3 pages and 4 pages exist? Or is that to be assumed?

thats what i thought and the answer came out to be D


Let's analyze the scenarios where there can be either 0 chapters with 3 pages or 0 chapters with 4 pages.

If there are 0 chapters with 3 pages:
x=0
x=0, and the equation becomes
4y=18
4y=18, which doesn't have a positive integer solution for y

If there are 0 chapters with 4 pages:
y=0
y=0, and the equation becomes
3x=18
3x=18, which doesn't have a positive integer solution for x.
In both cases, if one of the quantities is 0, the other quantity doesn't yield a positive integer solution. Therefore, both cases are not valid solutions

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brother, 3x=18, in this scenario x does have a positive integer solution
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