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24 Feb 2019, 23:58
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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:
25%
(medium)
Question Stats:
71% (00:59) correct
29%
(01:04)
wrong
based on 409
sessions
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Not Attempted Yet
If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?
A. \(\frac{n}{2}\)
B. \(\frac{n}{3}\)
C. \(\frac{n}{6}\)
D. \(\frac{n}{10}\)
E. \(\frac{n}{12}\)
A. \(\frac{n}{2}\)
B. \(\frac{n}{3}\)
C. \(\frac{n}{6}\)
D. \(\frac{n}{10}\)
E. \(\frac{n}{12}\)
21 Aug 2020, 23:02
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Let us take 6 and prime factorize it.
6 = 3x2 ------- (1)
So, definitely n will have one 3 and one 2 as it's prime factors.
Now, it is mentioned that n is not divisible by 4.
Let us take 4 and prime factorize it.
4 = 2x2 ------- (2)
From this, it is clear that "n" only has one 2 as its prime factor.
Coming to the options
1. Integer. Since n has one 2 as it's prime factor
2. Integer. Since n has one 3 as it's prime factor
3. Integer. Since n is divisible by 6.
4. Integer. Prime factorizing 10, we have 10 = 5x2. From here, we are sure that n does have one 2. If we plug in any value which has one 2 and one 5 as prime factors, then dividing by 10 results in an integer value.
For example, let's take n = 30. Since 30 is divisible 6 and not by 4 and at the same time prime factorizing 30, we get 30 = 2x3x5. In this case, dividing 30 by 10 results in an integer.
5. Not integer. If we prime factorize 12, then 12 = 2x2x3. This has two 2's. But n cannot have two 2's as its prime factors. So, this is the answer.
Answer E
6 = 3x2 ------- (1)
So, definitely n will have one 3 and one 2 as it's prime factors.
Now, it is mentioned that n is not divisible by 4.
Let us take 4 and prime factorize it.
4 = 2x2 ------- (2)
From this, it is clear that "n" only has one 2 as its prime factor.
Coming to the options
1. Integer. Since n has one 2 as it's prime factor
2. Integer. Since n has one 3 as it's prime factor
3. Integer. Since n is divisible by 6.
4. Integer. Prime factorizing 10, we have 10 = 5x2. From here, we are sure that n does have one 2. If we plug in any value which has one 2 and one 5 as prime factors, then dividing by 10 results in an integer value.
For example, let's take n = 30. Since 30 is divisible 6 and not by 4 and at the same time prime factorizing 30, we get 30 = 2x3x5. In this case, dividing 30 by 10 results in an integer.
5. Not integer. If we prime factorize 12, then 12 = 2x2x3. This has two 2's. But n cannot have two 2's as its prime factors. So, this is the answer.
Answer E
General Discussion
25 Feb 2019, 00:41
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Bunuel
n is divisible by 6 NOT by 4.
n = 6, 18, 30, 42, 54.
E is the correct answer.
