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JanGuillou
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Does there exist an integer d such that x > d > 1 & x/d is an integer? 29 Mar 2019, 04:19
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Dear all,

How do you know that there is no prime number among 11!+2 and 11!+12? I don't really get that. I tried it with 5!+2 - 5!+12 but there are prime number in between.

Thus, could you please provide a detailed explanation?

Thank you very much, your help is highly appreciated.

Best,
Jan
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tannumunu
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Does there exist an integer d such that x > d > 1 & x/d is an integer? 27 Apr 2020, 13:51
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ENGRTOMBA2018
noyaljoseph
Does there exist an integer d such that x > d > 1 and x/d is an integer?

(1) 11! + 2 < x < 11!+ 12
(2) x > 2^5

The very requirement of this question to find whether x has another integer such that x/d is an integer is the very definition of a prime number 'x ' that does not have an integer 'd' such that x/d is an integer.

Thus the question is simply asking whether 'x' is a prime number.

Per statement 1, you can very well see that 11!+2 will be divisible by 2 (as 11! = 1*2*3 ....10*11) and similarly all numbers from 11!+2 to 11!+ 12 will all be composites (or not prime). This this statement is sufficient.

Per statement 2, x > 2^5. Clearly not sufficient as there will always be a prime number greater than a given number (without any other bounds). Not sufficient.

Thus A is the correct answer.

Hope this helps.
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Hi,

Your explanation is clear. Yet I have one doubt. In this DS we have to answer whether "d" is integer or not.
From statement 1- it is clear that "x" is composite. Given condition x>d>1 and x/d is integer. If I take Value of X as 11!+3 and if I divide "x" with d where value of "d" is 0.3 then also "x/d" is an integer but "d" is not an integer.
Can you please correct my doubt or if I am with any misconception.
Thanks
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Does there exist an integer d such that x > d > 1 & x/d is an integer? 14 Mar 2024, 01:00
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