Data Sufficiency

Currently there are 50 picture books
each shelf in the children's section of
a library. 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 of these
books ?
(1) The number of smaller shelves
needed is 6 more than the current
number of shelves.
(2) Currently there are 9 shelves in
the children's section.

If we call x the number of current shelves and y the number of smaller shelves, then 50x will be the current number of books distributed on the x shelves and 30y would be the number of books on y shelves. Since the # of books is the same in both cases, we have 1 linear equation: 50x = 30y

The question asks for how many of the smaller shelves are needed: What is y?

Statement 1:
y (# of smaller shelves) is 6 more than x (# of current shelves), so y = x+6. Note that this gives us a 2nd linear equation. Combined with 50x=30y, we have 2 distinct linear equations and 2 variables, so we could solve for y (and x) and thus answer the question.

[spoiler](1) is sufficient[/spoiler].

Statement 2:
x = 9. Plugging that into 50x = 30y would allow us to find y.
[spoiler]
(2) is sufficient[/spoiler].

D is correct.

In the shelve with 50 books each
Total books = 50X

In the shelve with 30 books each
Total books = 50Y

Both of these should be same i.e 50X = 30Y.

i) y = x+6
50X = 30(X+6)
X = 9
Sufficient

ii) X = 9
50X = 30 Y
Replace x value
Y = 15.

Both A& D are sufficient