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

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

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Updated on: 03 Apr 2012, 23:52
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55% (hard)

Question Stats:

61% (01:36) correct 39% (01:41) wrong based on 249 sessions

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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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

Originally posted by Smita04 on 03 Apr 2012, 19:48.
Last edited by Bunuel on 03 Apr 2012, 23:52, edited 1 time in total.
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03 Apr 2012, 20:53
4
KUDOS
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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03 Apr 2012, 22:30
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..
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Joined: 28 Feb 2012
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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

Therefore, the only answer choice left out is 5.

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

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16 Apr 2012, 03:51
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 three-digit prime number and j is an integer [#permalink]

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16 Apr 2012, 04:37
1
KUDOS
Expert's post
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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 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.

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

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09 Nov 2013, 04:53
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 three-digit prime number and j is an integer [#permalink]

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10 Nov 2013, 04:33
monirjewel wrote:
Can anyone provide the list of three digit prime numbers?
picking number is the only way to solve this question?

Check here: if-n-is-a-three-digit-prime-number-and-j-is-an-integer-130199.html#p1074281

To get the list of 3-digit primes Google it but memorizing the list is complete waste of time.
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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.

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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.

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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.
Re: If n is a three-digit prime number and j is an integer   [#permalink] 26 Mar 2017, 01:18
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