Currently there are 50 picture books on each shelf in the children's

let bigger shelves =x
smaller shelves = y
total nu of books before = 50*x
total nu of books afterwards = 30*y
st 1 : y=x+6
so, 50(x)=30(x+6) hence we can find the nu of shelves.
st : 2 x=9, so find nu of total books then divide by 30.

hence each one is sufficient, ANS D.

Solution

Given:

• Currently 50 picture books are there in each shelf in the children’s section

To find:

• How many shelves would be required if each shelf has 30 books

Analysing Statement 1

• As per the information given in statement 1, the number of smaller shelves needed is 6 more than the current number of shelves

o If n is the current number of shelves, then number of smaller shelves will be (n + 6)
o As per the information, \(50 * n = 30 * (n + 6)\)
o Solving this, we can find out the value of n

Hence, statement 1 is sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, currently there are 9 shelves
• If we assume there would be x shelves after rearrangement, we can say

o \(50 * 9 = 30 * x\)
o Solving this, we can find out the value of x

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option D.

Answer: D


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Alternate Method

Information given: Currently there are 50 picture books on each shelf in the children's section of a library.

Question: If these books were to be placed on smaller shelves with 30 picture books on each shelf, how many of the smaller shelves would be needed to hold all these books?

Statement (1): The number of smaller shelves needed is 6 more than the current number of shelves.

We are going to shelves of 30 books each.

From the original set of shelves, we are going to the same number of shelves + 6.

We are essentially taking 20 books off each of the original number of shelves and putting them on 6 shelves of 30.

6 x 30 = 180

180/20 = the original number of shelves = 9

Number of smaller shelves needed 9 + 6 = 15

Sufficient.

Statement (2): Currently there are 9 shelves in the children's section.

Using this statement along with the information provided in the question we can determine the total number of books, which we could divide by 30 to get the number of smaller shelves needed.

Sufficient.

The correct answer is (D).
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One question on the phrasing of the opening statements: "smaller shelves with 30 picture books on each shelf"
Do we assume that each shelf MUST have 30 books and the last shelf can't have, say, less than 30 books?
For example -- say we had 100 books. Shelves needed earlier = 100/50 = 2
Now, for rows of 30 each, shelves needed = 100/30 --> 3+1 (to keep the remaining 10 books) = 4

Is this not an acceptable case here? The language of the question does not seem clear to me in that sense..

Notice that the question says, "Currently, there are 50 picture books on each shelf."

Then, for the second situation, it says, "30 picture books on each shelf."

So, the statements don't say, "Each shelf CAN hold 50 books," or "each shelf CAN hold 30 books," leaving open the possibility that there are some shelves with fewer than 50 or 30 books on them. Rather, the question specifies the exact number of books "on each shelf."

Thus, we know that all the books are on shelves in sets of exactly 50 or 30 per shelf.
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Let x be the number of shelves, so...
50(x) = total number of books

According to statement 1, we need 6 more shelves to fit the total number of books so...
30(x+6) = total number of books

Equating the two equations...
50(x) = 30(x+6)
50x = 30x + 180
20x = 180
x = 9 shelves

Therefore, we need x+6 smaller shelves i.e. 9 + 6 = 15 shelves. Sufficient

Statement 2 essentially tells us that x = 9, which means we can calculate the total number of books: 50 x 9 = 450

450 total books / 30 books per shelf = 15 shelves. Also sufficient