lheiannie07 wrote:If x and y are greater than 1, is the largest prime factor of x greater than the largest prime factor of y?
(1) x = 7^n
(2) The least common multiple of x and y is 105.
Which of the statement is sufficient?
OA E
Statement 1 is clearly not sufficient, as we have nothing about y. If x = 7 and y = 2, we get a YES, if x = 7 and y = 11, we get a NO.
Statement 2: 105 = 3 * 5 * 7. We know that between x and y, there must be a 3 and a 5 and a 7. And neither can have more than one of these prime bases within its prime factorization.
Case 1: x = 7, y = 3*5; The answer here is YES, the greatest prime factor of x is larger than the greatest prime factor of y.
Case 2: x = 7; y = 3*5*7; The answer here is NO, the greatest prime factor of x is not larger than the greatest prime factor of y.
Notice that when we're testing together, we can use those same cases, thus generating a YES and a NO. Together the statements are not sufficient to answer the question. The correct answer is
E
