Data Sufficiency Hard 4

If x < 0, is y > 0?
(i) x/y < 0 (ii) y – x > 0

Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?
(i) Each member’s contribution is to be $4.
(ii) If 5 club members fail to contribute, the share of each contributing member will increase by $2.

Is 5k less than 1,000 ?
(i) 55 + 1 > 3,000
(ii) 5k – 1 = 5k – 500

If n is a positive integer, is the value of b – a at least twice the value of 3n – 2n ?
(i) a = 2n – 1 and b = 3n + 1
(ii) n = 3

If x is an integer, is x|x|< 2x ? (i) x < 0 (ii) x = - 10

If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?
(i) Rafael has more than 5 tapes.
(ii) Carmen has fewer than 12 tapes.

If n is a positive integer and k = 5.1×10n, what is the value of k ?
(i) 6,000 < k < 500,000 (ii) k2= 2,601× 109

In the expression above, if xn≠0, what is the value of S ?
(i) x = 2n
(ii) n = 1/2

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ? (i) The coordinates of point Q are (13,0). (ii) The coordinates of point P are (6,8).

If x and y are positive, then x is what percent of y?
(i) 15 is 25 percent of y.
(ii) x is 10 percent of 2y.