Data Sufficiency

What is the value of n in the equation: - 25 + 19 + n = s ? (1) s = 2 (2) n/s = 4

In any twenty-four-hour period, a certain faulty clock gains anywhere from one second to a maximum of three minutes. The clock did not stop or lose time since noon the day before yesterday. At exactly noon today, did the clock show the correct time to an accuracy of five minutes? (1) The clock was set to the correct time the day before yesterday at exactly noon. (2) At exactly noon yesterday, the clock was set back by one minute.

If arc PQR above is a semicircle, what is the length of diameter PR ? (1) a = 4 (2) b = 1

The couple decide one day that they will definitely go to the beach the next evening if it is sunny without rain at the time they plan to go, and that they will definitely not go if such is not the case. The next morning, the hour-by-hour weather forecast says that in the evening, it will be sunny without rain. Will the couple go to the beach that evening? (1) It is raining on the morning and in the afternoon of the day of their planned beach outing. (2) The couple always believe that the weather forecast is likely to be accurate.

A small library has books on twenty different subjects including, most prominently, history. One afternoon, a librarian arbitrarily picks up $100$ books for reshelving from among the books returned that day. All the books returned that day were borrowed during the past three weeks. Are fewer than $20$ percent of the books the librarian picks up on history? (1) Fewer than $20$ percent of the books in the library are on history. (2) During the past three weeks, exactly $15$ books on history were borrowed from the library.

In the figure above, what is the value of x + y ? (1) x = 70 (2) ABC and ADC are both isosceles triangles

Four book lovers have recently met and are not sure of the topics that interest the others. The table indicates the topics that interest each of them with check marks and those that do not with cross marks (Xs). One of these persons will gift another of these persons two books, each on a different one of the listed topics. Will at least one of the two books fall under the recipient's broad topic of interest? (1) One topic is science fiction and the other is humor. (2) The intended recipient is Carlos.

In a gas sample, there are, rounded to the nearest order of magnitude (that is, to the nearest power of $10$), approximately $10^{21}$ molecules of ${\mathrm{H}}_2$ and also $10^{21}$ molecules of ${\mathrm{O}}_2$. What is the combined number of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ molecules in the gas sample, rounded to the nearest order of magnitude? (1) The number of ${\mathrm{H}}_2$ molecules and the number of ${\mathrm{O}}_2$ molecules are each less than $3\times 10^{21}$. (2) The number of ${\mathrm{H}}_2$ molecules is more than twice the number of ${\mathrm{O}}_2$ molecules.

What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price? (1) The number of tickets sold at the full price was 1/4 of the total number of tickets sold. (2) The full price of a ticket was $25.

On Jane's credit card account, the average daily balance for a $30$-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the $30$ days. At the beginning of a certain $30$-day billing cycle, Jane's credit card account had a balance of $\$600$. Jane made a payment of $\$300$ on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle? (1) Jane's payment was credited on the 21st day of the billing cycle. (2) The average daily balance through the 25th day of the billing cycle was $\$540$.

While on a straight road, Car X and Car Y are traveling at different constant rates. If Car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y ? (1) Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour. (2) Three minutes ago Car X was 1/2 mile ahead of Car Y.

The annual rent collected by a corporation from a certain building was $x$ percent more in $1998$ than in $1997$ and $y$ percent less in $1999$ than in $1998$. Was the annual rent collected by the corporation from the building more in $1999$ than in $1997$? (1) $x>y$ (2) $\frac{xy}{100}<x-y$

During an experiment, some water was removed from each of $6$ water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was $10$ gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment? (1) For each tank, $30$ percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment. (2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was $63$ gallons.

What is the average (arithmetic mean) of j and k ? (1) The average (arithmetic mean) of j + 2 and k + 4 is 11. (2) The average (arithmetic mean) of j, k, and 14 is 10.

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish? (1) Of the 300 students, 60 do not study Spanish. (2) A total of 240 of the students study Spanish.

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot? (1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ? (1) The price of the Model K mixer was $102.40 more in 1989 than in 1970. (2) The price of the Model K mixer was $142.40 in 1989.

Is x a negative number? (1) 9x > 10x (2) x + 3 is positive.

S = 2 n 1 x + 2 3 x S = 2 n 1 x + 2 3 x In the expression above, if xn ≠ 0, what is the value of S? (1) x = 2n (2) n = 1/2

If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael? (1) Rafael has more than 5 tapes. (2) Carmen has fewer than 12 tapes.