Was the number of books sold at Bookstore X last week greater than the

A ] Does not tell us anything about the sales in the rest of the week .INSUFFICIENT

B] Does not tell us 20% of what , hence we cannot compare . INSUFFICIENT

Together

Let sales at bookstore X on saturday be 1001 . Therefore >5005 books were sold in the week

Let sales at bookstore Y on saturday be 999. Therefore <4995 books were sold during the week

Hence we can conclude that sales at X were greater than Y for the given week

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.

Knowing the number of books that were sold on one day of the week is not enough information to determine whether, for the entire 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 how many books were sold last week at 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 on Saturday (note: s > 1,000)

t = the number of books sold at Bookstore Y on Saturday (note: t < 1,000)

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 q > p, and all values are positive, we can determine that sq is greater than pt, and thus that x > y.

Answer: C
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yosita18
I am posting the reply to PM here as it may help others as well.

Let me rephrase the analysis in simpler terms.

Statement 1 : Analysis

Store X: more than 1000 books sold. Say for our consideration, 1001.
Store Y: less than 1000 books sold. Say for our consideration, 999.

This stmt is insufficient since we dont know the sales on other days of the week.

Statement 2: Analysis

Store X: Less than 20% of all the books sold for the week was sold on Saturday. [Say Store X made a sale of 19% of all the books sold over the week.]
Store Y: More than 20% of all the books sold for the week was sold on Saturday. [Say Store Y made a sale of 21% of all the books sold over the week.]

This statement is not sufficient to tell us anything as we cant deduce the accurate figures just on this statement alone.

Combining both the statements:
As going by our example, Store X sold 1001 books which is 19% of overall sales. Therefore, total sale: \(1001 * \frac{100}{19}\)
Similarly, for store Y; total sale: \(999 * \frac{100}{21}\)

Clearly total sales at Bookstore X is more. Hence C.

Hope this helps.
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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

OG has the best explanation hands down...

We are looking to answer if Tx > Ty where Tx and Ty represent Total Books x and Total Books Y respectively

Statement (1): Xsat > 1000 and Ysat < 1000 - Insufficient

Statement (2): Xsat < 0.2Tx and Ysat > 0.2Ty - Insufficient


Combining both statements we have:

For Bookstore X: 1000 < Xsat < 0.2Tx this can be simplified 1000 < 0.2Tx divide both sides by 0.2 gives Tx > 5000

For Bookstore Y: 0.2Ty < Ysat < 1000 this can be simplified 1000 > 0.2Ty divide both sides by 0.2 gives Ty < 5000

Therefore C

The take away message from this exercise is that you should know that when you have something like a < x < b then a, x < b which means that you can generate two independent inequalities from a compound inequality with 3 terms (i.e. a < b and x < b) . The rest of the question is simply read carefully and translate the words into maths/equation/inequalities.

amanvermagmat niks18 chetan2u




I could not understand why ans is C and not E.
The question stem talks about finding no of books in TOTAL WEEK and each statement talks about only SAT.
What if from Mon to Fri book sales are reverse than mentioned in St 2?
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Hi

We dont necessarily have to find the total number of books last week for X and Y. All we need is a comparison between books sold at X and books sold at Y last week.

Books at X on Saturday > 1000, and these are less than 20% (or less than 1/5) of books sold in entire week. This means books sold in entire week in X > 5*1000 or number of books in X in entire week > 5000

Also books at Y on Saturday < 1000, and these are more than 20% (1/5) of books sold in entire week. So this number is less than 1000, but more than 1/5 of total week. IF this number was 1000 and exactly equal to 1/5 of total, then the total books would have been = 5*1000 = 5000. But here the books sold in Y in entire week will be less than 5000.

So, even though we are unable to determine the exact number of books sold in X and in Y - we at least know for sure that for X the number is > 5000 and for Y the number is < 5000. Hence Sufficient.

For those of you who are stuck with c, you are wondering why c is correct, here is a nice way to deal with such questions
Let books sold at X be x
Let books sold ay Y be y
Greater than 1000====> Test values 1001, 1010
Less than 1000======> Test values 999, 990

1) (20/100) * x = 1001
x = 5005
2) (20/100) * y = 999
y = 4995
So here x > y
but wait, test one more value to look for pattern that where the values of x and y are going
Let x = 1010 and y = 990
1) (20/100) * x = 1010
x = 5050
2) (20/100) * y = 990
y = 4950

Now analyze the pattern, x is getting bigger and y is getting smaller so the gap between them is getting bigger as well. They will never meet. So x is always > y
So C is the answer

Hello Bunuel !

Can you help me please?

I attached 2 notes, and they refer my process of thinking.

However, I have a doubt about 1)&2) part.. Can I just directly judge the answer in that way without the verification?

Thank you in advance!!

Answer: Option C

Video solution by GMATinsight



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Both statements alone are clearly insufficient.

1+2

let the total # of books sold at X for the whole week= x
let the total # of books sold at Y for the whole week = y

1+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.

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

cool, let's assume, 15 % less sales occurred at X on Saturday and 25 % more sales occurred at Y on Saturday.

.85 (x) = something greater than 1000
1.25 (y) = something less than 1000

x= number greater than 1000/.75

y= number less than 1000/1.25


we can see, in y Numerator is decreasing and denominator is increasing. However, in x numerator will increase and denominator will decrease. so, without knowing exactly by how many % did the actual decrease and increase in sales happened on Saturday, we can say, for a fact, x will always be greater than

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