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22 Apr 2025, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
53% (01:16) correct
47%
(01:14)
wrong
based on 287
sessions
History
Date
Time
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Not Attempted Yet
If n is the product of 2, 3, and a two-digit prime number, how many of its factors are greater than 6?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
22 Apr 2025, 02:11
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Bunuel
n = 2*3*ab
ab could be {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ....}
Let, Ab = 2*3*11
factors of n greater than 6 = 11 and 2*11 and 3*11 and 2*3*11
i.e. 4 factors
Answer: Option D
Related Video:
General Discussion
22 Apr 2025, 06:37
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If n is the product of 2, 3, and a two-digit prime number, how many of its factors are greater than 6?
A. 1
B. 2
C. 3
D. 4
E. 5
We have been asked how many factors are there in 2 * 3 * x that are greater than 6.
(‘x’ is a two - digit prime number)
We know that ‘x’ is a factor of the number ‘n’ and that it has two digits, meaning that ‘x’ is 1 factor bigger than 6.
‘n’ is a factor of itself and it HAS to be bigger than 6, meaning that we have now found 2 factors bigger than 6.
2*3*x = 6*x = n
We know that 6 has been multiplied by a two - digit number , meaning that 2 and 3 which are also factors of ‘n’ and are smaller than 6 must be multiplied by a number larger than ‘x’ to yield ‘n’, meaning that we have 2 more factors bigger than 6.
We can’t have any more factors bigger than 6 as ‘n’ has been prime factorised.
Hence answer = 4 = D
We can’t have any also solve this by substituting any prime number greater than 7 and then list out all the possible factors.
A. 1
B. 2
C. 3
D. 4
E. 5
We have been asked how many factors are there in 2 * 3 * x that are greater than 6.
(‘x’ is a two - digit prime number)
We know that ‘x’ is a factor of the number ‘n’ and that it has two digits, meaning that ‘x’ is 1 factor bigger than 6.
‘n’ is a factor of itself and it HAS to be bigger than 6, meaning that we have now found 2 factors bigger than 6.
2*3*x = 6*x = n
We know that 6 has been multiplied by a two - digit number , meaning that 2 and 3 which are also factors of ‘n’ and are smaller than 6 must be multiplied by a number larger than ‘x’ to yield ‘n’, meaning that we have 2 more factors bigger than 6.
We can’t have any more factors bigger than 6 as ‘n’ has been prime factorised.
Hence answer = 4 = D
We can’t have any also solve this by substituting any prime number greater than 7 and then list out all the possible factors.
