Inequalities

If x and y are positive, is x < 10 < y? (1) x < y and xy = 100 (2) x^2 < 100 < y^2

If xy ≠ 0, is x^3 + y^3 > 0 ? (1) x + y > 0 (2) xy > 0

If x and y are integers, is x > y? (1) x + y > 0 (2) y^x < 0

If a and b are positive integers, is a/b < 9/11 ? (1) a/b < 0.818 (2) b/a > 1.223

If q, s, and t are all different numbers, is q < s < t ? (1) t - q = |t - s| + |s - q| (2) t > q

What is the value of x if x^3 < x^2? (1) –2< x < 2 (2) x is an integer greater than –2.

If u > 0 and v > 0, which is greater, u v u v or v u v u ? (1) u = 1 (2) v > 2

Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14

If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9

If n is an integer, is ( 0.1 ) n ( 0.1 ) n greater than ( 10 ) n ( 10 ) n ? (1) n > − 10 n > − 10 (2) n < 10 n < 10

If a, b, c, and d, are positive numbers, is a b < c d a b < c d ? (1) 0 < ( c − a ) ( d − b ) 0 < ( c − a ) ( d − b ) (2) ( a d b c ) 2 < ( a d ) ( b c ) ( a d b c ) 2 < ( a d ) ( b c )

If r > 0 and s > 0, is r/s < s/r? (1) r/(3s) = 1/4 (2) s = r + 4

If r and s are the roots of the equation x^2 + bx + c = 0, where b and c are constants, is rs < 0 ? (1) b < 0 (2) c < 0

If 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y, is 3(2.00X) > 2(3.00Y) ? (1) 3X < 2Y (2) X < Y − 3

If a and b are integers, is a 5 < 4 b a 5 < 4 b ? (1) a 3 = – 27 a 3 = – 27 (2) b 2 = 16 b 2 = 16

Is the average (arithmetic mean) of the numbers x, y, and z greater than z ? (1) z − x < y − z (2) x < z < y

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

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

Which of the positive numbers x or y is greater? (1) y = 2x (2) 2x + 5y = 12

If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5? (1) The units digit of a is 4. (2) The units digit of b is 7.