A bookshelf holds both paperback and hardcover books. The

First of all it should be \(202\leq{P+H}\leq{247}\).

Next, we'll get \(177.76\leq{P}\leq{217.36}\). From 22H=3P we know that P must be a multiple of 22. There is only one multiple of 22 in that range: 198.

Not a good way to solve.

Hi All,

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:

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

Given: We can solve this question easily by ratio grid. Given that bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3.


To find: The number of paperback books is on the shelf!!!
Analysis of statement 1: The number of books on the shelf is between 202 and 247, inclusive.


As the total number of books must be the multiple of 25, there is only one value between 202 and 247 i.e. 225. Therefore it’s very easy to fill up the ratio grid now!!
So, the statement 1 is sufficient to answer. We can eliminate option B,C and E.
Analysis of 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.
We can form the equation as ((22x-18))/((3x+18))= 4/1

22x-18=12x+72
10x=90;x=9
Therefore number of paperback books will be 22 ×x=22 × 9=198.
So, the statement 2 is sufficient to answer. We can eliminate option B.
The correct answer option is “D”.

I tried something similar:
1.
202<\(\frac{25h}{3}\)<247
24,24<h<29,64

We get that h might be:
25
26
27
28

h must be divisible by 3 (p=\(\frac{22h}{3}\))
25
26
27
28
29

Hence: sufficient

Hello Friends!
main concepts to know here are the multiples (In this case multiples of 25) and how to solve set of two linear equations

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