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22 Jun 2023, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:36) correct
33%
(01:22)
wrong
based on 54
sessions
History
Date
Time
Result
Not Attempted Yet
Is the number of distinct prime factors of the positive integer N more than 4?
(1) N is a multiple of 42.
(2) N is a multiple of 98.
(1) N is a multiple of 42.
(2) N is a multiple of 98.
22 Jun 2023, 01:48
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(1) Only
If N = 42, It contains three distinct prime factors: 2,3,7.
If N = 42*41*43, it contains five distinct prime factors: 2,3,7, 41, 43
Insufficient
(2) Only
If N = 98, it contains two distinct prime factors: 2, 7
If N = 98 * 41 * 43 * 97, it contains five distinct prime factors: 2, 7, 41, 43, 97
Insufficient
(1)(2) Together
N has to be a multiple of 294 = 2 * 3 * 7 * 7
If N = 294, it contains three distinct prime factors: 2, 3, 7
If N = 294*41*43, it contains five distinct prime factors: 2,3,7, 41, 43
Insufficient.
The answer is thus (E).
If N = 42, It contains three distinct prime factors: 2,3,7.
If N = 42*41*43, it contains five distinct prime factors: 2,3,7, 41, 43
Insufficient
(2) Only
If N = 98, it contains two distinct prime factors: 2, 7
If N = 98 * 41 * 43 * 97, it contains five distinct prime factors: 2, 7, 41, 43, 97
Insufficient
(1)(2) Together
N has to be a multiple of 294 = 2 * 3 * 7 * 7
If N = 294, it contains three distinct prime factors: 2, 3, 7
If N = 294*41*43, it contains five distinct prime factors: 2,3,7, 41, 43
Insufficient.
The answer is thus (E).
22 Jun 2023, 03:07
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(1) N is a multiple of 42.
The prime factorization of 42 is 2 * 3 * 7. If N is a multiple of 42, it means N can have at least these prime factors. However, it is possible for N to have additional prime factors beyond 2, 3, and 7. Without knowing more about the prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on statement (1) alone. Statement (1) is not sufficient.
(2) N is a multiple of 98.
The prime factorization of 98 is 2 * 7 * 7. If N is a multiple of 98, it means N can have at least these prime factors. Again, it is possible for N to have additional prime factors beyond 2 and 7. Without further details about the prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on statement (2) alone. Statement (2) is not sufficient.
Considering both statements together:
By combining the two statements, we know that N is a multiple of both 42 and 98. This implies that N must have at least the prime factors of 2, 3, and two 7's. However, we still don't have specific information about other prime factors of N. Without knowing the complete prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on the combination of statements (1) and (2). The combination is not sufficient.
E
The prime factorization of 42 is 2 * 3 * 7. If N is a multiple of 42, it means N can have at least these prime factors. However, it is possible for N to have additional prime factors beyond 2, 3, and 7. Without knowing more about the prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on statement (1) alone. Statement (1) is not sufficient.
(2) N is a multiple of 98.
The prime factorization of 98 is 2 * 7 * 7. If N is a multiple of 98, it means N can have at least these prime factors. Again, it is possible for N to have additional prime factors beyond 2 and 7. Without further details about the prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on statement (2) alone. Statement (2) is not sufficient.
Considering both statements together:
By combining the two statements, we know that N is a multiple of both 42 and 98. This implies that N must have at least the prime factors of 2, 3, and two 7's. However, we still don't have specific information about other prime factors of N. Without knowing the complete prime factorization of N, we cannot determine if the number of distinct prime factors is more than 4 based on the combination of statements (1) and (2). The combination is not sufficient.
E
