If x and y are positive integers, what is the value of xy?

(1) The greatest common factor of x and y is 10.
(2) The least common multiple of x and y is 180.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Company X has n regional offices, where n represents an even integer. Each regional office must recommend two candidates, one male and one female, to serve on the corporate auditing committee. If each of the offices must be represented by exactly one member on the auditing committee and if the committee must consist of an equal number of male and female employees, how many different committees can be formed?

(A) Square of (.5n)
(B) n!/(Square of ((.5n)!))
(C) Square of (n!/((0.5n)!(.5n)!)))
(D) n!/((0.5n)!)
(E) n!

If x= 3y , is x^2 > y^2 ?

1 ) y+x > y-x
2) x^2 = 9y^2

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

The Question has been edited

from x2-y2 => x^2 – y^2

————————————–

Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

m is a positive integer >0. f(m) = 3m for every odd value of m, m=(1/2)m for every even value of m. f(9) * f(6) ?

a) 81
b) 64
c) 27
d) 9
e) 6

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

This sentence was marked as correct in Manhattan Sentence correction.  can any one please explain as to how is it justified.

A majority of railway commuters reads or listens to music while travelling.