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If n is a three-digit prime number and j is an integer [#permalink]

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03 Apr 2012, 19:48

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If n is a three-digit 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?

Option a, b and c satisfy the 3-digit 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..

Re: If n is a three-digit prime number and j is an integer [#permalink]

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04 Apr 2012, 04:58

if n = xyz and Prime then z = 1, 3, 7 ; And 5j = ...-20, -15, -10, -5, 0, 5, 10, 15, 20, ....

if z = 1, n-5j will yield the unit digit as either 1 or 6 if z = 3, n-5j will yield the unit digit as either 8 or 3 if z = 7, n-5j will yield the unit digit as either 2 or 7

Re: If n is a three-digit prime number and j is an integer [#permalink]

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05 Apr 2012, 02:33

Smita04 wrote:

If n is a three-digit 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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Can anyone explain it better? Not sure why, but I am not able to get this :D

If n is a three-digit 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

\(n-5j = k\) --> \(n=k+5j\). 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 three-digit prime number), then prime number \(n\) cannot be a multiple of 5, so \(k\) cannot equal to 5.

Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Re: If n is a three-digit prime number and j is an integer [#permalink]

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13 Dec 2013, 11:44

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 3-digit prime number. So considering equation k=n-5j 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.

Re: If n is a three-digit prime number and j is an integer [#permalink]

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05 Jan 2015, 02:20

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Re: If n is a three-digit prime number and j is an integer [#permalink]

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19 Jun 2016, 08:34

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If n is a three-digit prime number and j is an integer [#permalink]

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22 Mar 2017, 19:07

Smita04 wrote:

If n is a three-digit 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 three-digit 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 three-digit prime number by 5?

Well, a three-digit 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 three-digit prime number and j is an integer [#permalink]

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26 Mar 2017, 01:18

If n is a three-digit 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 n-5j=k if k=5 the n-5j=5 or n-5j-5= n-5(j+1)=0.

Substitute values in this and we get that this does not give a definitve value. E is correct.