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If n is a threedigit prime number and j is an integer [#permalink]
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03 Apr 2012, 18:48
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If n is a threedigit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
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Last edited by Bunuel on 03 Apr 2012, 22:52, edited 1 time in total.
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Re: Threedigit prime number [#permalink]
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03 Apr 2012, 19:53
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E is the correct answer because if k = 5, then n = 5j + 5 = 5(j+1) => n is a multiple of 5, which contradicts what is stated in the question Also, examples for other choices : 101  5* 20 = 1 103  5*20 = 3 107  5 * 21 = 2 109  5 * 21 = 4
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Re: Threedigit prime number [#permalink]
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03 Apr 2012, 21:30
Option a, b and c satisfy the 3digit prime number crteria only for certain conditions..fo eg in n=5J+1, if I substitute J with 21, the value of n that I get is 106 which is not prime..The sam is true for b and c also..Please advise if I am getting it wrong somewhere..



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Re: If n is a threedigit prime number and j is an integer [#permalink]
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04 Apr 2012, 03:58
if n = xyz and Prime then z = 1, 3, 7 ; And 5j = ...20, 15, 10, 5, 0, 5, 10, 15, 20, ....
if z = 1, n5j will yield the unit digit as either 1 or 6 if z = 3, n5j will yield the unit digit as either 8 or 3 if z = 7, n5j will yield the unit digit as either 2 or 7
Therefore, the only answer choice left out is 5.
The answer is E.



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Re: If n is a threedigit prime number and j is an integer [#permalink]
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05 Apr 2012, 01:33
Smita04 wrote: If n is a threedigit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Its pretty straight forward; if k=5 it means n is a multiple of 5=> cant be prime hence E
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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16 Apr 2012, 02:51
Can anyone explain it better? Not sure why, but I am not able to get this :D
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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16 Apr 2012, 03:37
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ENAFEX wrote: Can anyone explain it better? Not sure why, but I am not able to get this :D If n is a threedigit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k?A. 1 B. 2 C. 3 D. 4 E. 5 \(n5j = k\) > \(n=k+5j\). Now, if \(k=5\) then \(n=5+5j=5(1+j)\), so we have that \(n\), which is a prime number, is a multiple of 5. But since given that \(n>5\) (\(n\) is a threedigit prime number), then prime number \(n\) cannot be a multiple of 5, so \(k\) cannot equal to 5. Answer: E.
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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09 Nov 2013, 03:53
Can anyone provide the list of three digit prime numbers? picking number is the only way to solve this question?
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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13 Dec 2013, 10:44
Bunuel answer the best logical answer for this question but I would like add something with common understanding rather than digging deep into logic of prime numbers and factors.
Whatever be the value of j. 5J=5,10,15,20..... I mean a multiple of 5 ending in 5 or 0. N could be any 3digit prime number. So considering equation k=n5j difference cannot be 5 or multiple of 5 because for that case N cannot be a prime number.
This what Question asked NOT a possible value of K.
Answer is E



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If n is a threedigit prime number and j is an integer [#permalink]
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22 Mar 2017, 18:07
Smita04 wrote: If n is a threedigit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that \(n – 5j = k\) ?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 OFFICIAL SOLUTION Rearrange the equation for k to isolate n: \(n = 5 j + k\) You are told that k is to be the “smallest positive integer” that makes this equation true for some threedigit prime number n, given that j is an integer. This equation may remind you of remainders (especially if you glance at the answer choices). Since j is an integer, the term 5 j just means “multiple of 5.” The integer k is defined to be positive, so instead of 0 as the remainder, you have 5 as its replacement. So you’re “sort of” being asked this: which of the following numbers CANNOT be the remainder after you divide a threedigit prime number by 5? Well, a threedigit prime number cannot be a multiple of 5. The only prime number that is a multiple of 5 is 5 itself, which only has one digit. So n cannot be written as 5 j + 5. Every other remainder is a possibility: 101, 103, 107, and 109 in fact are all primes, and they give you 1, 3, 2, and 4 as possible values of k. The correct answer is E.
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Re: If n is a threedigit prime number and j is an integer [#permalink]
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26 Mar 2017, 00:18
If n is a threedigit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
This question can be solved by substitution method and use 101,103,107.... values.
Now n5j=k if k=5 the n5j=5 or n5j5= n5(j+1)=0.
Substitute values in this and we get that this does not give a definitve value. E is correct.




Re: If n is a threedigit prime number and j is an integer
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