The number of hardcover books at bookstore X is 67.5% of all the books

(1) There is the same number of books at both stores. insufic

hx+nx=hy+ny…x/y=1

(2) There are 20,000 more hardcover books at bookstore X than there are at bookstore Y. insufic

hx=hy+20k;

(1,2) sufic

hx=hy+20k…67.5%x=66.9%y+20k…(x=y)…67.5%x-66.9%x=20k…x=20k/0.6%

Ans (C)

The number of hardcover books at bookstore X is 67.5% of all the books at the store, while the number of hardcover books at bookstore Y is 66.9% of all the books in that store. How many hardcover books are at bookstore Y?

(1) There is the same number of books at both stores.
(2) There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.

There are two book stores X and Y. Total number of books of X and Y stores are not mentioned here.
From statement (1), we know that the two stores contain same number of books but not any specific number.
If we say both stores contain 100 books each, then around 70 hardcover books are found in Y.
If we say both stores contain 200 books each, then around 140 hardcover books are found in Y.
Not sufficient.

From statement (2), we cannot say total number of books in the stores X and Y. Not Sufficient.

Combining both statements, we cannot determine the number of hardcover books at bookstore Y.
Not sufficient. Answer: E

#1
There is the same number of books at both stores.
clearly insufficient as value of books would vary with each value of total books
#2
There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.
.675x= 20,000+ .695*y
but x& y are not know insufficient
from 1 &2
.675x-.695x= 20,000
books at x & y can be known
sufficient
IMO C



The number of hardcover books at bookstore X is 67.5% of all the books at the store, while the number of hardcover books at bookstore Y is 66.9% of all the books in that store. How many hardcover books are at bookstore Y?

(1) There is the same number of books at both stores.
(2) There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.

Let \(t\) be the total number of books at bookstore X and let \(t'\) be the total number of books at bookstore Y.

From the given information, we know that:

The number of hardcover books at bookstore \(X=0.675t\)
The number of hardcover books at bookstore \(Y=0.669t'\)

The question asks us to find the value of \(0.669t'\). Hence, to answer the question, we need to find the value of \(t'\).

Statement 1:
There is the same number of books at both stores.

This essentially tells us that \(t=t'\). But we don't know the value, so we can't answer the question with this information. INSUFFICIENT.

Statement 2:
There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.

This gives us the following equation: \(0.675t + 20000 = 0.669t'\), however, there are two unknowns here, so we still can't answer the question with this information. INSUFFICIENT.

Combining both statements:
Since \(t=t'\), we can solve for one variable and get the value for \(0.669t\). SUFFICIENT. Remember, once we know for sure that we can solve for the answer with the given information, we should pick our answer and move on.

C is our answer.

Hope this helps!

Let the number of books at store X & Y be 'a' & 'b' respectively
--> Number of hardcover books at X = 0.675a & at Y = 0.669b

(1) There is the same number of books at both stores.
--> a = b
We cannot find the number of hardcover books = 0.669b using the above information
--> Insufficient

(2) There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.
--> 0.675a = 20000 + 0.669b
--> Does not say anything about the value of b --> Insufficient

Combining (1) & (2),
a = b & 0.675a = 20000 + 0.669b
--> 0.675b - 0.669b = 20,000
--> 0.006b = 20,000
--> We can the value of b & then the number of hardcover books in store Y = 0.675b --> Sufficient

Option C

Let the hardcover books at Bookshop X be Xh and other books at X be Xo. Let the hardcover books at Y be Yh and other books be Yo.
We are informed that Xh=67.5% of all books at X and Yh=66.9% of all books at Y. We are to determine Yh.

Statement 1: There is the same number of books at both stores.
if x is the total number of books at X and y is the total number of books at Y, then x=y according to statement 1. This is insufficient since we have no way of determining how many books are there in X or Y.

Statement 2: There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.
Xh=Yh+20,000, implying 0.675x=0.669y+20000 ---------(1)
Insufficient because we need to know the relationship between x and y before we can determine Yh=0.669y

1+2
Sufficient because we now know the relationship between x and y; i.e. x=y
Hence 0.675x=0.669x+20,000
We can, therefore, determine x=y and Yh=0.669y.

The answer is C.

(1) There is the same number of books at both stores.......clearly insufficient to find the no.of hardcover books...INSUFFICIENT
(2) There are 20,000 more hardcover books at bookstore X than there are at bookstore Y.....By just knowing the difference we cannot compare both bookstore....INSUFFICIENT

Combining both we get the diff = 20000
(67.5%-66.9%) of total books = 20000
sufficient

OA:C