Last visit was: 21 Nov 2024, 18:24 It is currently 21 Nov 2024, 18:24

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [8]
Given Kudos: 25927
Send PM
avatar
Intern
Intern
Joined: 19 Apr 2023
Posts: 1
Own Kudos [?]: 3 [3]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [1]
Given Kudos: 25927
Send PM
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
1
Expert Reply
OE

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
avatar
Intern
Intern
Joined: 25 Aug 2023
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 1
Send PM
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
1
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
Intern
Intern
Joined: 10 Jul 2023
Posts: 12
Own Kudos [?]: 8 [1]
Given Kudos: 29
Send PM
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
1
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

Posted from my mobile device
Manager
Manager
Joined: 05 Sep 2023
Posts: 63
Own Kudos [?]: 66 [1]
Given Kudos: 11
Send PM
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
1
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.
avatar
Intern
Intern
Joined: 19 Oct 2023
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 0
Send PM
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
2
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

Posted from my mobile device


brother, 3x=18, in this scenario x does have a positive integer solution
Prep Club for GRE Bot
Re: An 18 pages long book comprises either of 3 pages or 4 pages long chap [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne