Data Sufficiency

When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result? (1) The player tossed the coin 24 times. (2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

Last year, a certain company began manufacturing Product X and sold every unit of Product X that it produced. Last year, the company's total expenses for manufacturing Product X were equal to $\$100,000$ plus $5$ percent of the company's total revenue from all units of Product X sold. If the company made a profit on Product X last year, did the company sell more than $21,000$ units of Product X last year? (1) The company's total revenue from the sale of Product X last year was greater than $\$110,000$. (2) For each unit of Product X sold last year, the company's revenue was $\$5$.

If the two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? (1) Each step is 3/4 foot high. (2) Each step is 1 foot wide.

Beginning in January of last year, Carl made deposits of $\$120$ into his account on the 15th of each month for several consecutive months and then made withdrawals of $\$50$ from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $\$2,600$, what was the range of the monthly closing balances of Carl's account last year? (1) Last year, the closing balance of Carl's account for April was less than $\$2,625$. (2) Last year, the closing balance of Carl's account for June was less than $\$2,675$.

What is the value of integer n? (1) n(n+1) =6 (2) 2^(2n) = 16

What amount did Jean earn from the commission on her sales in the first half of $1988$? (1) In $1988$, Jean's commission was $5$ percent of the total amount of her sales. (2) The amount of Jean's sales in the second half of $1988$ averaged $\$10,000$ per month more than in the first half.

In a certain business, production index $p$ is directly proportional to efficiency index $e$, which is in turn directly proportional to investment index $i$. What is $p$ if $i=70$? (1) $e=0.5$ whenever $i=60$. (2) $p=2.0$ whenever $i=50$.

Is rst = 1 ? (1) rs = 1 (2) st = 1

The annual rainfall in a city over the past $50$ years is its historical average rainfall (HAR). The graph shows the annual rainfall in City X over a seven-year period. All figures are rounded to the nearest integer. Is it true that the rounded HAR for City X is $47$ mm or greater? (1) In the seven-year period in City X, the annual rainfall was greater than the HAR in exactly two of the consecutive years. (2) In the seven-year period in City X, the annual rainfall was less than the HAR in exactly four of the years.

Five coffee-chicory blends—J, K, L, M, and N—are all priced differently. The blends are such that the greater the proportion of coffee, the more expensive the blend, and the greater the proportion of chicory, the stronger the flavor of the blend. If the five blends were ranked in order of cost per kilogram, which would fall in the middle? (1) Blend L has a higher proportion of coffee than the other blends except for Blend M. (2) Blend K and Blend N both have a stronger flavor than Blend J.

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees? (1) Exactly 100 of the employees are college graduates. (2) Of the employees 40 years old or less, 25 percent have master's degrees.

Last summer, as with every summer, Oshin and Reena made exactly one long trip together to a town neither of them had visited before. For their long summer trips, Oshin and Reena have always chosen to visit a town that Reena would have liked to visit—unless Oshin had been to that town before. Reena had visited Town F and Town G before, and Oshin had never visited Town J or Town K. Did Oshin and Reena visit one of these four towns last summer? (1) Reena had never visited Town J, and Oshin had never visited Town F. (2) Oshin would have liked to visit either Town G or Town K.

What percent of the drama club members enrolled at a certain school are female students? (1) Of the female students enrolled at the school, 40 percent are members of the drama club. (2) Of the male students enrolled at the school, 25 percent are members of the drama club.

For a new project, an organization is creating a three-member team from among its employees. Selection of members for the team conforms to exactly two rules: no selected member can be working on more than one other project at the time of selection, and at least one of the selected members must have an MBA degree. The organization has selected Paula and Quincy for the team. Neither of these will be replaced before the third member is selected. The organization is about to make the third selection. If the organization adheres to the selection rules for committee membership, is it possible that Rubin will be selected for the team? (1) Quincy has an MBA degree, and Rubin is currently working on only one other project. (2) Rubin is one of only two employees in the organization who have an MBA degree.

All the T-shirts a clothing store stocks are plain, and they are all in one of exactly four colors: blue, green, red, and yellow. On any given day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts? (1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined. (2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

The table shows the sales forecast from January to June of last year, by the sales team of Company X, for the number of units of Product Z each month. Was the actual number of units of Product Z sold in March less than the number sold in April? (1) Twelve units of Product Z were sold in March. (2) From January through June of last year, there was a constant, linear relationship between the forecast and actual number of units of Product Z sold.

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class? (1) Of the boys in the class, 15 are studying biology. (2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Chris was in an electronic appliances store to buy an LED computer monitor. Chris's purchase criteria included screen size, which must be at least $32$ inches, and price, which must not exceed $\$400$. A friend made two recommendations: Monitor A and Monitor B. Chris liked both monitors. Did Chris more likely buy Monitor A, Monitor B, or neither? (1) Monitor A's screen size was more than $32$ inches and it cost less than Monitor B. (2) Monitor B cost $\$390$ and its screen size was less than that of Monitor A.

Is n an integer? (1) n 2 n 2 is an integer (2) √ n n √ is an integer

A certain pizzeria has more than fifty types of pizza on its menu. The chart shows the revenue share, in the pizzeria's total revenue in the last month, of its four most popular pizza types. Each pizza type has only a single size and a single price. Which was their best-selling pizza last month in terms of number of pizzas sold? (1) The number of customers who ordered at least one Pep-Peroni pizza last month was greater than the number of customers who ordered at least one of any other pizza type last month. (2) The lowest-priced pizza type on the pizzeria's menu is Tomato Blast, followed by VegCheese.