Data Sufficiency

For a basic monthly fee of F yen, Noako's first cell phone allowed him to use a maximum of 420 minutes on calls during the month. Then, for each of x additional minutes he used on calls, he was charged M yen, making his total charge for the month T yen, where T = F + xM. What is the value of M? (1) Naoko used 450 minutes on calls the first month and the total charge for the month was 13, 755 yen (2) Naoko used 400 minutes on calls the second month and the total charge for the month was 13, 125 yen Moderator Note: This version of the question is different from DS #278 in OG2017

If x and y are positive integers, is xy even? (1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd.

A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the pentagon greater than 26 centimeters? (1) The area of the circle is 16π square centimeters. (2) The length of each diagonal of the pentagon is less than 8 centimeters.

If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12.

Is w + h 4 w + h 4 positive? (1) h is positive (2) w is positive

Is the positive two-digit integer N less than 40 ? (1) The units digit of N is 6 more than the tens digit. (2) N is 4 less than 4 times the units digit.

Do at least 60 percent of the students in Pat’s class walk to school? (1) At least 60 percent of the female students in Pat’s class walk to school. (2) The number of students in Pat’s class who walk to school is twice the number of students who do not walk to school.

Is x + 1 y + 1 > x y x + 1 y + 1 > x y ? (1) 0 < x < y 0 < x < y (2) x y > 0 x y > 0

If w + z = 28, what is the value of wz (1) w and z are positive integers (2) w and z are consecutive odd integers (1) w and z are positive integers (2) w and z are consecutive odd integers

What is the value of t? (1) s + t = 6 + s (2) t^3 = 216

Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5

In the figure above, is the area of triangular region ABC equal to the area of triangular region DBA ? (1) (AC)^2=2(AD)^2 (2) ∆ABC is isosceles. Source: OG13

A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank? (1) The inside of the tank is exactly 4 feet in diameter. (2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet. From OG 2016 (question 86 DS)

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle? (1) The area of the triangle is 25 square centimeters. (2) The 2 legs of the triangle are of equal length.

In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C ? (1) A + 2B + C = 24 (2) A + C = 18 and B = 3

Is the point Q on the circle with center C ? (1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. (2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C.

y = ax - 5 y = x + 6 y = 3x + b In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b? (1) a = 2 (2) r = 17

Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length.

In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term? (1) The last term is 90. (2) The first term is 2.

What is the area of triangular region ABC above? (1) The product of BD and AC is 20. (2) x = 45