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If x and y

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If x and y

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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

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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

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