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For an integer n greater than 1, n* denotes the product
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26 Mar 2015, 03:07
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64% (01:36) correct 36% (02:08) wrong based on 203 sessions
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For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ? A. 0 B. 1 C. 2 D. 3 E. 4
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Re: For an integer n greater than 1, n* denotes the product
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26 Mar 2015, 03:47
Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7. Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range. Answer: A. Similar questions to practice: foranyintegerngreaterthan1ndenotestheproductof168575.htmlforanyintegermgreaterthan1mdenotestheproductof148722.htmlforanyintegerppisequaltotheproductofalltheint112494.htmlforanyintegerngreaterthan1ndenotestheproductof131199.htmlforanyintegerkgreaterthan1thesymbolkdenotesthe105890.htmldoestheintegerkhaveafactorpsuchthat1pk126735.htmlifxisanintegerdoesxhaveafactornsuchthat100670.html
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Re: For an integer n greater than 1, n* denotes the product
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26 Mar 2015, 04:58
Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 None. as 7! is multiple of all numbers in the set \({1,2,3,4,5,6,7}\) so when you add any of these number to the 7! you will always a multiple of one the numbers in the set. similar question : doestheintegerkhaveafactorpsuchthat1pk126735.html



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Re: For an integer n greater than 1, n* denotes the product
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27 Mar 2015, 06:48
Bunuel wrote: Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7. Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range. Answer: A Hi Bunuel, Based on the concept you mentioned that we can take a factor out from each number which results in no prime numbers between 7!+2 and 7!+7, can we say that if we add to 7! a number which is not a factor of 7* then the resultant number will be prime no.? e.g. can we say 7!+11 or 7!+13 are prime numbers? Thanks in advance.



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Re: For an integer n greater than 1, n* denotes the product
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27 Mar 2015, 07:07
gmatkiller88 wrote: Bunuel wrote: Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7. Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range. Answer: A Hi Bunuel, Based on the concept you mentioned that we can take a factor out from each number which results in no prime numbers between 7!+2 and 7!+7, can we say that if we add to 7! a number which is not a factor of 7* then the resultant number will be prime no.? e.g. can we say 7!+11 or 7!+13 are prime numbers? Thanks in advance. Hi gmatkiller88, Not necessarily so. Here is a counter example, 3! + 19 = 25, not prime.



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Re: For an integer n greater than 1, n* denotes the product
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27 Mar 2015, 08:10
shreyast wrote: gmatkiller88 wrote: Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
Hi Bunuel,
Based on the concept you mentioned that we can take a factor out from each number which results in no prime numbers between 7!+2 and 7!+7, can we say that if we add to 7! a number which is not a factor of 7* then the resultant number will be prime no.?
e.g. can we say 7!+11 or 7!+13 are prime numbers? Thanks in advance. Hi Not necessarily so. Here is a counter example, 3! + 19 = 25, not prime. gmatkiller88, Ok. So I guess in such cases we need to check each number individually to decide if the number is prime or not. Thanks.



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Re: For an integer n greater than 1, n* denotes the product
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19 Feb 2016, 05:27
I did it this way 7!+2=2(7*6*5*4*3*1+1)=this will not be prime 7!+3=3(7*6*5*4*2*1+1)=this will not be prime ....... 7!+7=7(7*6*5*4*2*1+1)=same,not prime as it is multiple of 7 answer=0/A +1 for kudosssss
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Re: For an integer n greater than 1, n* denotes the product
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08 May 2018, 06:40
Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 7* = 7! = (7)(6)(5)(4)(3)(2)(1)So, 7* + 2 = (7)(6)(5)(4)(3)( 2)(1) + 2= 2[(7)(6)(5)(4)(3)(1) + 1] = some multiple of 2So, 7* + 2 is NOT a prime number 7* + 3 = (7)(6)(5)(4)( 3)(2)(1) + 3= 3[(7)(6)(5)(4)(2)(1) + 1] = some multiple of 3So, 7* + 3 is NOT a prime number 7* + 4 = (7)(6)(5)( 4)(3)(2)(1) + 4= 4[(7)(6)(5)(3)(2)(1) + 1] = some multiple of 4So, 7* + 4 is NOT a prime number . . . . 7* + 7 = ( 7)(6)(5)(4)(3)(2)(1) + 7= 7[(6)(5)(4)(3)(2)(1) + 1] = some multiple of 7So, 7* + 7 is NOT a prime number ASIDE: You can assume that I was able to perform the same steps with 7* + 5 and 7* + 6 Answer: A Cheers, Brent
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Re: For an integer n greater than 1, n* denotes the product
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12 Aug 2019, 11:49
Turkish wrote: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
A. 0 B. 1 C. 2 D. 3 E. 4 Notice that n* (which is the same thing as n!) is divisible by all positive integers from 1 to n. 7* + 2 is divisible by 2 (since both 7* and 2 are divisible by 2) 7* + 3 is divisible by 3 (since both 7* and 3 are divisible by 3) … In general, 7* + k is divisible by k when k is between 2 and 7, inclusive (since 7* is divisible by k and k is divisible by k). Therefore, none of the numbers between 7* + 2 and 7* + 7, inclusive, is a prime. Answer: A
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Re: For an integer n greater than 1, n* denotes the product
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