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OG - number of books sold

This topic has 2 expert replies and 0 member replies
fiza gupta Master | Next Rank: 500 Posts
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OG - number of books sold

Post Tue Nov 15, 2016 12:36 am
Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week?

(1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday
(2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday

OA:C

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Fiza Gupta

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Post Wed Nov 16, 2016 8:08 am
fiza gupta wrote:
Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week?

(1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday
(2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday

OA:C
We need to determine whether the number of books sold at Bookstore X last week was greater than the number of books sold at Bookstore Y.

Statement One Alone:

Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday.

Only knowing the number of books that were sold on one day of the week is not enough information to determine whether, for the whole week, the number of books sold at Bookstore X was greater than the number of books sold at Bookstore Y. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday.

Since we do not know how many books were sold on Saturday, we cannot determine much about how many books were sold last week from either Bookstore X or Bookstore Y.

Statements One and Two Together:

Using the information from statements one and two, we can define the following variables:

x = the number of books sold at Bookstore X last week

y = the number of books sold at Bookstore Y last week

s = the number of books sold at Bookstore X Saturday (note: s > 1000)

t = the number of books sold at Bookstore Y Saturday (note: t < 1000)

p = percent of books at Bookstore X sold last week that were sold on Saturday (note: p < .2)

q = percent of books at Bookstore Y sold last week that were sold on Saturday (note: q > .2)

Using our variables we can create the following equations:

x = s/p

and

y = t/q

We need to determine whether x > y, or s/p > t/q, or sq > pt. Since s > t and p < q, we can determine that sq is greater than pt, and thus x > y.

Answer: C

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Jeffrey Miller Head of GMAT Instruction

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Top Reply
Post Tue Nov 15, 2016 4:48 am
fiza gupta wrote:
Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week?

(1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday
(2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday

OA:C
Clearly, neither statement alone is sufficient.

Statements combined:
Test the THRESHOLD VALUES.
Here, the threshold values are 1000 books and 20% of the total.

X:
If 1000 books are equal to 20% of the total number of books, we get:
1000 = (20/100)X
X = (1000*100)/20.
X = 5000.
Implication:
If the red value = 1000 and the blue value = 20, X = 5000.
Since the red value is actually GREATER THAN 1000, while the blue value is actually LESS THAN 20, X > 5000.

Y:
If 1000 books are equal to 20% of the total number of books, we get:
1000 = (20/100)Y
Y = (1000*100)/20.
Y = 5000.
Implication:
If the red value = 1000 and the blue value = 20, Y = 5000.
Since the red value is actually LESS THAN 1000, while the blue value is actually GREATER THAN 20, Y < 5000.

Thus:
Y < 5000 < X
Y < X.
SUFFICIENT.

The correct answer is C.

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For more information, please email me at GMATGuruNY@gmail.com.

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