Data Sufficiency Questions (Inequalities and Modulus)

1) is sqrt ((x-3)^2) = 3-x?1) x not equal to 32) -x|x| > 0

2) What is the value of y?

(1) 3|x^2 – 4| = y – 2(2) |3 – y| = 11

3) If xy+z=z, is |x-y|>0?1. x# 0 (Not equal to)2. Y= 0

4) Whether x>y>z?(1) x-y = |x-z|+|z-y|(2) x > y

5) Whether x>y>z?(1) x-y = |x-z|+|z-y|(2) x > y

6) Is x^1/2 a prime number? (1) mod (3x-7) = 2x+2 (2) x^2 = 9x

7) if zy<xy<0 is Ix-zI+IxI=IzI1) Z<x2) Y>0

8) If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0 (2) ab > 0 (ab is greater than or equal to zero)

9) If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x(2) |x| > x

10) How many factors does the integer X have?

1. X^(x+3) = (2x)^(x-1)2. |3x-7| = 2x+2

11) Is |x| < 1?

(1) |x + 1| = 2|x - 1| (2) |x - 3| ≠ 0

12) w, x, y, and z are integers. If z > y > x > w, is |w| > x^2 > |y| > z^2?

(1) wx > yz (2) zx > wy

13) If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0 (2) ab >= 0

14) Is ?

(1) (2) -x|x| > 3

15) If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2 (2) |x^2 - |x|| = 2

16) Is a prime number?

(1)

(2)

17) Is |x| + |x -1| = 1?

(1) x ≥ 0(2) x ≤ 1

18) Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16(2) a=|b|+5

19) If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x(2) |x| > x

20) . Is x > 0?

(1) |x + 3| = 4x – 3(2) |x + 1| = 2x – 1

21) Is |x−5|>4?

(1) x^2 −4>0(2) x^2−1<0

22) Is |x-y|>|x|-|y| ?

(1) y < x(2) xy < 0

23) Is ?

(1) (2)

24) If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x (2) |x| > x

25) If |a| = b is a + b > ab ?

(1) a = -b(2) a = -3

26) Is |x - y|>|x - z|?

(1) |y|>|z|(2) x < 0

27) Is ?

(1)

(2)

28) If x^2 = y^2, is true that x>0?

(1) x=2y+1(2) y<= -1

29) |x|=|2y|, what is the value of x-2y?

(1) x+2y = 6(2) xy>0

30) Is x > 0?

(1) |x + 3| = 4x – 3 (2) |x – 3| = |2x – 3|

31) If ab≠0, is

(1) |a| > |b| (2) (2) a < b

32) If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1(2) r < 1