Data Sufficiency

Of a group of 50 households, how many have at least one cat or at least one dog, but not both? (1) The number of households that have at least one cat and at least one dog is 4. (2) The number of households that have no cats and no dogs is 14.

If the Longfellow Playground is rectangular, what is its width? (1) The ratio of its length to its width is 7 to 2. (2) The perimeter of the playground is 396 meters.

What was Bill's average (arithmetic mean) grade for all of his courses? (1) His grade in social studies was 75, and his grade in science was 75. (2) His grade in mathematics was 95.

A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band? (1) x = 0.5 (2) The height of the tub is 1 meter. Show Spoiler

If 5x + 3y = 17, what is the value of x? (1) x is a positive integer (2) y = 4x

Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 liters. If the flow in each hose is independent of the flow in the other hose, how many hours will it take to fill the pool? (1) Hose X alone would take 28 hours to fill the pool. (2) Hose Y alone would take 36 hours to fill the pool.

If no student took test T more than once, how many students took test T ? (1) The average (arithmetic mean) of the students' scores on test T was 72. (2) The sum of he students' scores on test T was 2,232.

How many hours does it take 12 machines with identical production rates, running simultaneously without stopping, to fill a certain production order ? (1) It takes each machine alone, running continuously, 60 hours to fill the production order. (2) It takes 10 of these machines, running simultaneously without stopping, 6 hours to fill the production order.

If xy ≠ 0, is x/y < 0? (1) x = - y (2) -x = -(-y)

The table above shows the cancellation fee schedule that a travel agency uses to determine the fee charged to a tourist who cancels a trip prior to departure. If a tourist canceled a trip with a package price of $1,700 and a departure date of September 4, on what day was the trip canceled? (1) The cancellation fee was $595. (2) If the trip had been canceled one day later, the cancellation fee would have been $255 more. Show Spoiler

Is the number of members of Club X greater than the number of members of Club Y ? (1) Of the members of Club X, 20 percent are also members of Club Y. (2) Of the members of Club Y, 30 percent are also members of Club X.

If x = 2y, what is the value of xy ? (1) x > Y (2) 3x - 2y = 14

Is it true that a > b? (1) 2a > 2b (2) a + c > b + c

Yesterday Nan parked her car at a certain parking garage that charges more for the first hour than for each additional hour. If Nan’s total parking charge at the garage yesterday was $3.75, for how many hours of parking was she charged? (1) Parking charges at the garage are $0.75forthefirsthourand$0.50 for each additional hour or fraction of an hour. (2) If the charge for the first hour had been $1.00,Nan\hat{a}€™stotalparkingchargewouldhavebeen$4.00. Show Spoiler

In the figure above, if lines k and m are parallel, what is the value of x ? (1) y = 120 (2) z = 60 Show Spoiler

If n is a positive number, what is the value of n? (1) 1 + n = 5/4 (2) n^2 = 1/16

What is the value of the two-digit integer x ? (1) The sum of the two digits is 3. (2) x is divisible by 3. Show Spoiler

Is 5^k less than 1,000? (1) 5 (k+1) >3,000 (2) 5 (k−1) = 5 k −500

The government of Nation X makes policy decisions intended to advance the public interest, such as policy decisions aiming to promote employment, economic flourishing, and environmental protection. A policy decision can involve a significant trade-off, i.e., it can entail foreseeably giving up part or all of one valued outcome in the pursuit of another valued outcome. Does a policy decision by Nation X to permit extensive clearcutting of forests provide a valued outcome at the expense of another valued outcome? (1) Extensive clearcutting of forests is permitted in Nation X because it provides immediate economic gains by enabling businesses such as farming and lumbering to flourish and provide employment. (2) Extensive clearcutting of forests is permitted in Nation X even though it reduces forests’ absorption of carbon dioxide, and this indirectly contributes to global warming, resulting in adverse climate changes that are certain to be very costly for Nation X to manage.

Is William taller than Jane? (1) William is taller than Anna. (2) Anna is not as tall as Jane.