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13 Jan 2014, 04:57
Kudos
Bookmarks
E
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:
62% (01:54) correct
38%
(01:45)
wrong
based on 642
sessions
History
Date
Time
Result
Not Attempted Yet
Does the integer n have two factors, x and y, such that 1 < x < y < n?
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
Hi, I want to know if we have more simple solution for this question, please.
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
(1): 3! < n < 4! → 6 < n < 24. Every even integer can be expressed as a multiple of 2, all even numbers in range will give us a "yes" to question.
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
Hi, I want to know if we have more simple solution for this question, please.
13 Jan 2014, 06:31
Kudos
Bookmarks
goodyear2013
Does the integer n have two factors, x and y, such that 1 < x < y < n?
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
Hi, I want to know if we have more simple solution for this question, please.
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
(1): 3! < n < 4! → 6 < n < 24. Every even integer can be expressed as a multiple of 2, all even numbers in range will give us a "yes" to question.
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
Hi, I want to know if we have more simple solution for this question, please.
Does the integer n have two factors, x and y, such that 1 < x < y < n?
(1) 3! < n < 4! --> 6 < n < 24 --> If n=7=prime, then the answer is NO but if n=10, then the answer is YES. Not sufficient.
(2) n is odd and a multiple of 3. If n=3=prime, then the answer is NO but if n=15, then the answer is YES. Not sufficient.
(1)+(2) The same here: n=9=3^2 gives a NO answer, while n=15=3*5 gives an YES answer. Not sufficient.
Answer: E.
13 Jan 2014, 06:32
Kudos
Bookmarks
Bunuel
goodyear2013
Does the integer n have two factors, x and y, such that 1 < x < y < n?
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
Hi, I want to know if we have more simple solution for this question, please.
(1) 3! < n < 4!
(2) n is odd and a multiple of 3.
OE
(1): 3! < n < 4! → 6 < n < 24. Every even integer can be expressed as a multiple of 2, all even numbers in range will give us a "yes" to question.
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
However, since primes are in range (7, 11, 13, 17, 19, 23), that cannot be factored further than itself, we can also answer question "no."
If n = 8, it has 2 integer factors 2 and 4 that fit criteria: 1 < 2 < 4 < 8 → "yes"
If n = 7, it cannot be broken down into factors that fit criteria of question → "no"
Insufficient
(2): Any positive, odd multiple of 3 is a possible value for n. For larger multiples of 3, we can easily fit criteria, giving "yes" answer. However, since any number’s smallest multiple is itself, 3 is a possible value for n that would not fit criteria, giving "no."
If n = 15, we can factor it as 3 and 5, and we fit criteria: 1< 3 < 5 < 15 → "yes"
If n = 9, we can only factor it as 3 and 3, which does not fit criteria → "no"
Insufficient
Combined: (1) limits possible values of n to those integers between 6 and 24. (2) adds limitation that n be odd multiple of 3. Possible values for n = (9, 15 and 21)
If n = 9, we answer question "no,"
If n = 15 or 21, we can answer question "yes."
Insufficient
Hi, I want to know if we have more simple solution for this question, please.
Does the integer n have two factors, x and y, such that 1 < x < y < n?
(1) 3! < n < 4! --> 6 < n < 24 --> If n=7=prime, then the answer is NO but if n=10, then the answer is YES. Not sufficient.
(2) n is odd and a multiple of 3. If n=3=prime, then the answer is NO but if n=6, then the answer is YES. Not sufficient.
(1)+(2) The same here: n=9=3^2 gives a NO answer, while n=15=3*5 gives an YES answer. Not sufficient.
Answer: E.
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