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a, b, k, s are different non-zero integers, 2/a + 4/b = k/s and k/s is maximally reduced. Does s = ab?
1. a and b are primes
2. a and b have gcd = 1
  • a)
    Statement 1 alone is sufficient, but Statement 2 alone is not.
  • b)
    Statement 2 alone is sufficient, but Statement 1 alone is not.
  • c)
    Both statements together are sufficient, but neither alone is sufficient.
  • d)
    Each statement alone is sufficient.
  • e)
    Neither statement is sufficient.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
a, b, k, s are different non-zero integers, 2/a + 4/b = k/s and k/sis ...

Since k/s in its simplest form, s must be the denominator in its irreducible form, which is ab/gcd(2b + 4a,ab).
Statement 1: If a and b are primes, their product ab has no common factors with 2a + 4b (except possibly 2, but that won't affect the full fraction’s reducibility). Hence, s = ab.
Statement 2: If gcd (a, b) = 1, the same reasoning applies, as gcd(2b + 4a, ab) will still be 1. Thus, s = ab.
Since each statement alone guarantees the answer, the correct choice is D.
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