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16 Sep 2014, 00:16
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Is \(\frac{143}{z}\) an integer?
(1) \(z\) is a prime number
(2) \(8 < z < 17\)
(1) \(z\) is a prime number
(2) \(8 < z < 17\)
16 Sep 2014, 00:16
Kudos
Bookmarks
Official Solution:
Is \(\frac{143}{z}\) an integer?
(1) \(z\) is a prime number
Factorization gives 143 = 11*13. If \(z\) is either 11 or 13, then \(\frac{143}{z}\) will be an integer, but if \(z\) is any other prime number, then \(\frac{143}{z}\) will not be an integer. Thus, statement (1) alone is not sufficient to determine whether \(\frac{143}{z}\) is an integer or not.
(2) \(8 < z < 17\)
Some values of \(z\) in the given range make \(\frac{143}{z}\) an integer, while others do not. For instance, \(\frac{143}{11}\) is an integer, but \(\frac{143}{10}\) is not. Therefore, statement (2) alone is not sufficient to answer the question.
(1)+(2) Only the primes 11 and 13 satisfy \(8 < z < 17\), and for both of these values of \(z\), \(\frac{143}{z}\) is an integer. Therefore, when taken together, the statements are sufficient to determine whether \(\frac{143}{z}\) is an integer.
Answer: C
Is \(\frac{143}{z}\) an integer?
(1) \(z\) is a prime number
Factorization gives 143 = 11*13. If \(z\) is either 11 or 13, then \(\frac{143}{z}\) will be an integer, but if \(z\) is any other prime number, then \(\frac{143}{z}\) will not be an integer. Thus, statement (1) alone is not sufficient to determine whether \(\frac{143}{z}\) is an integer or not.
(2) \(8 < z < 17\)
Some values of \(z\) in the given range make \(\frac{143}{z}\) an integer, while others do not. For instance, \(\frac{143}{11}\) is an integer, but \(\frac{143}{10}\) is not. Therefore, statement (2) alone is not sufficient to answer the question.
(1)+(2) Only the primes 11 and 13 satisfy \(8 < z < 17\), and for both of these values of \(z\), \(\frac{143}{z}\) is an integer. Therefore, when taken together, the statements are sufficient to determine whether \(\frac{143}{z}\) is an integer.
Answer: C
General Discussion
