Data Sufficiency

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.

On a recent trip, Mary drove 50 miles. What was the average speed at which she drove the 50 miles? (1) She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour. (2) She drove a total of 54 minutes.

From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30? (1) If, during this period of time, the increase in the balance in the checking account had been $12$ percent, then the balance in the account on May 30 would have been $\$504$. (2) During this period of time, the increase in the balance in the checking account was $8$ percent.

The weights of all dishes of type X are exactly the same, and the weights of all dishes of type Y are exactly the same. Is the weight of 1 dish of type X less than the weight of 1 dish of type Y ? (1) The total weight of 3 dishes of type X and 2 dishes of type Y is less than the total weight of 2 dishes of type X and 4 dishes of type Y. (2) The total weight of 4 dishes of type X and 3 dishes of type Y is less than the total weight of 3 dishes of type X and 4 dishes of type Y.

A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount? (1) The percent discount on the coat was $2$ percentage points greater than the percent discount on the sweater. (2) Before the discounts, the sale price of the coat was $\$10$ less than the sale price of the sweater.

If the sequence S has 300 terms, what is the 293rd term of S? (1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term. (2) The first term of S is -22.

If the positive integer $n$ is added to each of the integers $69$, $94$, and $121$, what is the value of $n$? (1) $69+n$ and $94+n$ are the squares of two consecutive integers. (2) $94+n$ and $121+n$ are the squares of two consecutive integers.

If a < x < b and c < y < d, is x < y ? (1) a < c (2) b < c

If a merchant purchased a sofa from a manufacturer for $\$400$ and then sold it, what was the selling price of the sofa? (1) The selling price of the sofa was greater than $140$ percent of the purchase price. (2) The merchant's gross profit from the purchase and sale of the sofa was $\frac{1}{3}$ of the selling price.

Last year, in a certain housing development, the average (arithmetic mean) price of $20$ new houses was $\$160,000$. Did more than $9$ of the $20$ houses have prices that were less than the average price last year? (1) Last year, the greatest price of one of the $20$ houses was $\$219,000$. (2) Last year, the median of the prices of the $20$ houses was $\$150,000$.

In a random sample of 80 adults, how many are college graduates? (1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

For a certain city's library, the average cost of purchasing each new book is $\$28$. The library receives $\$15,000$ from the city each year; the library also receives a bonus of $\$2,000$ if the total number of items checked out over the course of the year exceeds $5,000$. Did the library receive the bonus last year? (1) The library purchased an average of $50$ new books each month last year and received enough money from the city to cover this cost. (2) The lowest number of items checked out in one month was $459$.

If $x$ is a number in the list $7,9,6,4,5,x$, what is the median of the list? (1) $x>7$ (2) The median of the list equals the arithmetic mean of the list.

Three dice, each of which has its $6$ sides numbered $1$ through $6$, are tossed. The sum of the $3$ numbers that are facing up is $12$. Is at least $1$ of these numbers $5$? (1) None of the $3$ numbers that are facing up is divisible by $3$. (2) Of the numbers that are facing up, $2$, but not all $3$, are equal.

Mohit went cycling on $10$ consecutive days. Every day he started from Point X, cycled a certain distance in an easterly direction, and then returned to Point X. What is the total distance he covered in those $10$ days? (1) From the second day onward, Mohit covered twice the distance he covered the previous day. On the fifth day, he covered $3.2$ km from Point X east, and then back to Point X. (2) On the first day, Mohit cycled less than $0.3$ km.

What is the cube root of w? (1) The 5th root of w is 64. (2) The 15th root of w is 4.

Candidates A, B, and C competed in an election. This election usually comprises two rounds. In the first round, all three candidates compete. A candidate qualifies for the second round only if he/she receives at least $20\%$ of the votes cast in the first round. If two candidates receive less than $20\%$ of the votes cast, the other candidate wins the election by default. If a candidate receives more than $60\%$ of the votes in the first round, he/she wins the election without the second round. Was there a second round of election? (1) The votes received by Candidates A and B together is $82\%$ of the total votes cast. (2) The votes received by Candidates C and B together is $42\%$ of the total votes cast.

Is 4 x + y = 8 10 4 x + y = 8 10 ? (1) x - y = 9 (2) y/x = 1/4

There are a certain number of male and female students in a classroom. The weights of the male students range from $80$ kg to $85$ kg. The weights of the female students range from $70$ kg to $75$ kg. What is the average (arithmetic mean) weight of all the students in the classroom? All weights are rounded to the nearest $1$ kg. (1) No two students weigh the same. (2) The number of male students is equal to the number of female students.

An alloy, Alloy K, is made by mixing certain quantities of iron and lead. The total weight of the alloy is $50$ kg. What is the ratio of the weight of iron to the weight of lead in Alloy K? (1) If $4$ kg of iron were to be replaced with $4$ kg of lead, the percentage of lead, by weight, in Alloy K would become $40\%$. (2) The weight of iron per $100$ cc is $0.7$ times the weight of lead per $100$ cc.