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
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