• Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

A bookshelf holds both paperback and hardcover books

This topic has 2 expert replies and 0 member replies

A bookshelf holds both paperback and hardcover books

Post Sun Nov 05, 2017 12:52 pm
A bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3. How many paperback books are on the shelf?

(1) The number of books on the shelf is between 202 and 247, inclusive.

(2) If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1

I am confused in the statements, can some experts help me identify if the statements are sufficient?

OA D

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Thu Nov 09, 2017 11:54 am
Hi lheiannie07,

We're told that the ratio of paperback books to hardcover books is 22 to 3. We're asked for the number of paperback books on the shelf. To start, we know that the number of paperback books MUST be a multiple of 22 and the number of hardcover books MUST be an equivalent multiple of 3. By extension, the TOTAL number of books MUST be a multiple of 25.

1) The number of books on the shelf is between 202 and 247, inclusive.

Fact 1 gives us a 'range' of possible totals. However, since the total number of books MUST be a multiple of 25, there's ONLY ONE option here: 225. We know that 22 out of every 25 books are paperbacks, thus the number of paperback books is (9)(22) = 198
Fact 1 is SUFFICIENT

2) If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1

With Fact 2, we can set up an equation based on the 'starting' number of books and the 'ending ratio of books:

Paperback/Hardcover = 22X/3X
After replacing 18 paperbacks with 18 hardcovers, we have...

(22X - 18)/(3X + 18) = 4/1

We can now solve for X...
22X - 18 = 12X + 72
10X = 90
X = 9

Therefore, the number of paperback books (22X) is (22)(9) = 198
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: lheiannie07

GMAT/MBA Expert

ErikaPrepScholar Master | Next Rank: 500 Posts
Joined
20 Jul 2017
Posted:
318 messages
Followed by:
4 members
Upvotes:
86
GMAT Score:
770
Most Active Expert Most Responsive Expert
Post Mon Nov 06, 2017 9:48 am
We know that the ratio of paperback to hardcover is 22 : 3 - this means that for every 25 books on the shelf, 22 will be paperback and 3 will be hardcover. It isn't possible to have part of a book, so we know that the total number of books must be divisible by 25. For instance, we could have 50 books, with 44 paperback and 6 hardcover, but we couldn't have 40 books, because then we would have 35.2 paperback and 4.8 hardcover.

Statement 1

There is only one multiple of 25 between 202 and 247: 225. This means that there must be (225 / 25) * 22 = 198 paperback books on the shelf. Sufficient.

Statement 2

If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1

Let's build an equation. If we have x groups of 25 books on the shelf:

22x - 18 : 3x + 18 = 4 : 1

Remember, we can always write ratios as fractions to more easily manipulate them:

$$\frac{22x\ -\ 18}{3x\ +\ 18}\ =\ \frac{4}{1}$$

22x - 18 = 12 x + 72
10 x = 90
x = 9

For every group of 9 books, there are 22 paperbacks, so there are 9 * 22 = 198 paperback books on the shelf. Sufficient.

_________________


Erika John - Content Manager/Lead Instructor
http://gmat.prepscholar.com/gmat/s/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our new PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: lheiannie07

Best Conversation Starters

1 Roland2rule 170 topics
2 lheiannie07 110 topics
3 ardz24 56 topics
4 LUANDATO 50 topics
5 swerve 48 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

155 posts
2 image description Scott@TargetTestPrep

Target Test Prep

122 posts
3 image description GMATGuruNY

The Princeton Review Teacher

121 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

110 posts
5 image description DavidG@VeritasPrep

Veritas Prep

81 posts
See More Top Beat The GMAT Experts