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If n is a prime number and n ≠ 3, which of the following [#permalink]
 03 Nov 2012, 01:49
Question Stats:
57% (01:40) correct
42% (00:53) wrong based on 3 sessions
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3? I. 0 II. 1 III. 2 A. II only B. III only C. I and II only D. II and III only E. I, II and III Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlbut the below idea wasn't mentioned You can add and subtract remainders directly, as long as you correct excess or negative remainders. " if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7. Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3 if n =1 remainder 1 so overall remainder is 1 if n = 2 remainder 2 so overall remainder is 2 if n = 6 remainder = 0 so overall remainder is 0 All 3 are possible right then why Princeton says D? Cheers.
Last edited by Bunuel on 03 Nov 2012, 01:55, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
03 Nov 2012, 01:59
Jp27 wrote: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3? I. 0 II. 1 III. 2 A. II only B. III only C. I and II only D. II and III only E. I, II and III Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlbut the below idea wasn't mentioned You can add and subtract remainders directly, as long as you correct excess or negative remainders. " if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7. Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3 if n =1 remainder 1 so overall remainder is 1if n = 2 remainder 2 so overall remainder is 2 if n = 6 remainder = 0 so overall remainder is 0 All 3 are possible right then why Princeton says D? Cheers. Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1. n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0. It can be 1 for n=7 and 2 for n=5. Answer: D. Hope it's clear.
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
03 Nov 2012, 02:14
Bunuel wrote: Jp27 wrote: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3? I. 0 II. 1 III. 2 A. II only B. III only C. I and II only D. II and III only E. I, II and III Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlbut the below idea wasn't mentioned You can add and subtract remainders directly, as long as you correct excess or negative remainders. " if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7. Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3 if n =1 remainder 1 so overall remainder is 1if n = 2 remainder 2 so overall remainder is 2 if n = 6 remainder = 0 so overall remainder is 0 All 3 are possible right then why Princeton says D? Cheers. Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1. n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0. It can be 1 for n=2 and 2 for n=5. Answer: D. Hope it's clear. ohh my god. Ok thanks.
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
03 Nov 2012, 08:30
Jp27 wrote: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3? I. 0 II. 1 III. 2 A. II only B. III only C. I and II only D. II and III only E. I, II and III Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlbut the below idea wasn't mentioned You can add and subtract remainders directly, as long as you correct excess or negative remainders. " if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7. Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3 if n =1 remainder 1 so overall remainder is 1 if n = 2 remainder 2 so overall remainder is 2 if n = 6 remainder = 0 so overall remainder is 0 All 3 are possible right then why Princeton says D? Cheers. My answer is D. if a number n is prime, and together with that does not equal 3 we can divide it on 3 whithout a remainder. 0 can't be the answer. we can also check it with, for example 5! and list of primes such as 2!,5!,7!... in your example if n = 6 - 6 is not prime
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
03 Nov 2012, 18:30
Bunuel wrote: Jp27 wrote: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3? I. 0 II. 1 III. 2 A. II only B. III only C. I and II only D. II and III only E. I, II and III Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlbut the below idea wasn't mentioned You can add and subtract remainders directly, as long as you correct excess or negative remainders. " if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7. Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3 if n =1 remainder 1 so overall remainder is 1if n = 2 remainder 2 so overall remainder is 2 if n = 6 remainder = 0 so overall remainder is 0 All 3 are possible right then why Princeton says D? Cheers. Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1. n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0. It can be 1 for n=2 and 2 for n=5. Answer: D. Hope it's clear. Hi, A minor correction in your post: for n=2, the remainder will be 2, not 1. for n=7, remainder will be 1. With respect, CJ
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
26 Nov 2012, 11:22
Another way to look at it is:
100!+n where n ≠ 3, since 100! will be a factor or 3, so we just have to care about n.
Hence, if n=2 then remainder of 2/3 is 2.
for any value of n>3, and n being prime it can be written as (6k+1) or (6k-1).
Hence, factor (6k+1)/3 will give remainder as 1, and (6k-1) would leave remainder as 2.
Please correct me if I am wrong.
Regards,
Nityam
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Re: If n is a prime number and n ≠ 3, which of the following [#permalink]
06 Apr 2013, 06:37
100! is divisible by 3. So we need to find out the remainder when the prime number n is divided by 3. For n = 2 or 5, remainder is 2. For n = 7, remainder is 1. n cannot be 3 as specified and cannot be any other multiple of 3 as n is prime. So the remainder cannot be 0. Answer is D.
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Re: If n is a prime number and n ≠ 3, which of the following
[#permalink]
06 Apr 2013, 06:37
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