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Bunuel
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Which of the following is a prime number? 28 Jul 2026, 19:01
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58% (01:10) correct 42% (01:18) wrong based on 89 sessions

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Which of the following is a prime number?

I. 9! + 5
II. 11! + 15
III. 13! + 13

A) I only
B) II only
C) III only
D) II and III only
E) None


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E
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dhart
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Which of the following is a prime number? Updated on: 28 Jul 2026, 23:47
Originally posted by dhart on 28 Jul 2026, 22:52.
Last edited by dhart on 28 Jul 2026, 23:47, edited 2 times in total.
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9! + 5 ( is a multiple of 90 + 5 = multiple of 5)

5( 9*8*7.....1+1) so , 5 is a factor
11! + 14 ( is a multiple of 110 + 15 = mulptiple of 1 and 5)

3*5 ( 11*10*9....1+1) so 1, 3 and 5 are factors

13! + 13 ( is a multiple of 130 + 13 , divisible by 1 and 13)

13(12*11*....1 + 1) so only 13 and 1 are factors
but primesare only divisibel by themselves and 1

the option is E
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Which of the following is a prime number? 28 Jul 2026, 23:10
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answer is E none since each three there is common term if there is common and is multiple of 2 terms , how can we say it is prime so none of them is prime. for example from I we can take common 5 from second we can take common 15 as 11! has 5*3 and from III we can take 13 common so all are product of 2 nos. none is prime

Bunuel
Which of the following is a prime number?

I. 9! + 5
II. 11! + 15
III. 13! + 13

A) I only
B) II only
C) III only
D) II and III only
E) None


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dhart
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Which of the following is a prime number? 28 Jul 2026, 23:29
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Welll i had'nt considered 13 as a extra factor caused it looked like a prime number lol now coreccted it though
odionam
answer is E none since each three there is common term if there is common and is multiple of 2 terms , how can we say it is prime so none of them is prime. for example from I we can take common 5 from second we can take common 15 as 11! has 5*3 and from III we can take 13 common so all are product of 2 nos. none is prime


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Which of the following is a prime number? 29 Jul 2026, 08:40
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I) 9! + 5
\(9!\) can be written as \(9*8*7*6*5*4!\)
Therefore, 9!+5 can be written as: \(5*(9*8*7*6*4!+1)\). We can see that the results of this sum has at least two different factor different from 1, so it's not a prime factor.


II) 11!+15
The idea is the same. 11! can be written as \(11*10*9*8!\), so the sum can be written as: \(11!+15=11*10*3*3*8!+15=3*(11*10*3*8!+5)\). Therefore, the result is not a prime factor.


III) 13!+13
Same idea. Let's rewrite 13! as \(13*12!\). Therefore, the sum can be also written as: \(13*(12!+1)\). The result is not a prime factor.


Answer: E
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Which of the following is a prime number? 29 Jul 2026, 11:59
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this can be solve by: N!+K, if k is less than equal to n then it is not prime no and vice versa.
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Bunuel
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