555-605 (Medium)
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?
(1) x - y = y - z
(2) x^2 - y^2 = z
705-805 (Hard)
The figure above represents an L-shaped garden. What is the value of k?
(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.
505-555 (Easy)
If m and n are integers, what is the value of m + n ?
(1) (x + m)(x + n) = x^2 + 5x + mn and x â 0.
(2) mn = 4
505-555 (Easy)
If r and s are positive numbers and θ is one of the operations, +, â, Ã, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0.
(2) If r â s, then r θ s â s θ r.
Sub 505 (Easy)
If sequence S has 120 terms, what is the 105th term of S?
(1) The first term of S is â8.
(2) Each term of S after the first term is 10 more than the preceding term. Source: [OG 2016]
505-555 (Easy)
If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81
(2) x â y = 2
655-705 (Hard)
In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?
(1) AB = 3 and BC = 2
(2) CD = 1 and DE = 4
605-655 (Medium)
In any sequence of n nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence â2, 3, â4, 5 has three sign changes. Does the sequence of nonzero numbers s1, s2, s3, . . . , sn have an even number of sign changes?
(1) s k = ( â 1 ) k s k = ( â 1 ) k for all positive integers k from 1 to n.
(2) n is odd.
555-605 (Medium)
Is zp negative?
(1) pz^4 < 0
(2) p + z^4 = 14
555-605 (Medium)
If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?
(1) s is a factor of 100
(2) r is a factor of 100
605-655 (Medium)
Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?
(1) v + z = 6
(2) s + t + u + x = 6
Sub 505 (Easy)
Is x an integer?
(1) x 3 = 8 x 3 = 8
(2) x = 4 â x = 4
Sub 505 (Easy)
If a + b + c = 12, what is the value of b ?
(1) a + b = 8
(2) b + c = 6
Sub 505 (Easy)
What is the value of 10 percent of y?
(1) 5 percent of y is 60.
(2) y is 80 percent of 1,500. Source: [OG 2016]
Sub 505 (Easy)
What is the number of pages of a certain journal article?
(1) The size of each page is 5 1 2 5 1 2 inches by 8 inches.
(2) The average (arithmetic mean) number of words per page is 250.
555-605 (Medium)
If a and b are integers, and b > 0, does a â 1 b + 1 = a b a â 1 b + 1 = a b ?
(1) a = b â 4
(2) a = âb
605-655 (Medium)
Two points, N and Q (not shown), lie to the right of point M on line l. What is the ratio of the length of QN to the length of MQ?
(1) Twice the length of MN is 3 times the length of MQ.
(2) Point Q is between points M and N.
655-705 (Hard)
Line â â lies in the xy-plane and does not pass through the origin. What is the slope of line â â ?
(1) The x-intercept of line â â is twice the y-intercept of line â â
(2) The x-and y-intercepts of line â â are both positive
555-605 (Medium)
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?
(1) s = 40
(2) r = 70
555-605 (Medium)
If x is a positive integer greater than 1, what is the value of x?
(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6