Inequalities

Is rw = 0? (1) −6 < r < 5 (2) 6 < w < 10 Source: [OG 2016]

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9? (1) y > 3x (2) y > x > 3

Is 5 x + 2 25 < 1 5 x + 2 25 < 1 ? (1) 5 x < 1 5 x < 1 (2) x < 0 x < 0

If x and y are integers, what is the value of x + y? (1) 3 < ( x + y ) 2 < 4 3 < ( x + y ) 2 < 4 (2) 2 < x < y < 5 2 < x < y < 5

If x + y z > 0 x + y z > 0 , is x<0? (1) x < y (2) z < 0

In the xy-plane, region R consists of all the points (x,y) such that 2 x + 3 y ≤ 6 2 x + 3 y ≤ 6 . Is the point (r,s) in region R? (1) 3 r + 2 s = 6 3 r + 2 s = 6 (2) r ≤ 3 r ≤ 3 and s ≤ 2 s ≤ 2

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

If x is an integer, what is the value of x ? (1) 1 5 1 5 < 1 ( x + 1 ) 1 ( x + 1 ) < 1 2 1 2 (2) ( x − 3 ) ( x − 4 ) ( x − 3 ) ( x − 4 ) = 0

Is x y < 0 x y < 0 ? (1) x 2 * y 3 < 0 x 2 * y 3 < 0 (2) x y 2 > 0 x y 2 > 0

If x ≠ − y x ≠ − y , then is x − y x + y > 1 x − y x + y > 1 ? (1) x > 0 x > 0 (2) y < 0 y < 0

Is 1 p > r r 2 + 2 1 p > r r 2 + 2 ? (1) p = r p = r (2) r > 0 r > 0

Is x equal to 5 ? (1) x ≥ 5 (2) x ≤ 5

Are positive integers p and q both greater than n ? (1) p - q is greater than n (2) q > p

Is 2x - 3y < x^2 ? (1) 2x - 3y = -2 (2) x > 2 and y > 0

If m > 0 and n > 0, is m + x n + x > m n m + x n + x > m n ? (1) m < n (2) x > 0

Is m ≠ n ? (1) m + n < 0 (2) mn < 0

If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4

Is k greater than t? (1) kt = 24 (2) k^2 > t^2

Is x y < 6 x y < 6 ? (1) x < 3 x < 3 and y < 2 y < 2 (2) 1 2 < x < 2 3 1 2 < x < 2 3 and y 2 < 64 y 2 < 64

Is |x| = y - z ? (1) x + y = z (2) x < 0