rohitgoel15 wrote:

Bill can dig a well in x! hours. Carlos can dig the same well in y! hours. If q is the number of hours that it takes Bill and Carlos to dig the well together, working at their respective rates, is q an integer?

(1) x - y = 1

(2) y is a nonprime even number.

B = \(\frac{1}{x!}\)

C = \(\frac{1}{y!}\)

Together = \(\frac{1}{q}\)

=> q = \(\frac{x!y!}{x!+y!}\)

q = Integer ?

1) x - y = 1

x = 3, y = 2

q is not an integer

x = 4. y = 3

q = \(\frac{4*3!*3!}{5*3!}\) = not integer

x = 5, y = 4 => q = 20 (Integer)

Insufficient.

2) y is an even number other than 2

Insufficient. We know nothing about x

1+2)

x - y = 1

and y = even except 2

=> for all even values of y, q = integer.

x = 5, y = 4 => \(\frac{5*4!*4!}{6*4!}\) = 20

x = 7, y = 6 => \(\frac{7*6!*6!}{8*6!}\) = 630

Sufficient. Answer is C

_________________

Put in the work, and that dream score is yours!