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

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.

The answer is E.

Its pretty straight forward;

if k=5 it means n is a multiple of 5=> cant be prime

hence E

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.

Answer: E.

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.

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.

Answer is E

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.

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.

n is a 3 digit prime number, so it can be anything from the smallest 101 to 997. However any number ending with 5 or 0 cannot be a prime number because it is divisible by 5.

5j is certainly a multiple of 5 and its last digit will be either 5 or 0.
hence if you subtract the 2 numbers, the answer can be 1,2,3,4 but NOT 5.

You can assume that 5J is the closest to the prime number.
eg. 101-5*20=1
or 997-5*199=2

either way the unit digit of the prime number can not be 5 more than 0 or 5, because then it would be divisible by 5.

We know that every prime, except for 2 and 5, ends in 1,3,7,9.

Know we can use this property and just focus on how the last digit (i.e. 1,3,7,9) changes when we suubstract 5.

1-5 = last digit becomes 6
3-5 = last digit becomes 8
7-5 = last digit becomes 2
9-5 = last digit becomes 4

These answer choices as well as the primes themselves can be eliminated.

Hence, 5 is the only answer that does not fit the bill.

Please hit Kudos if you liked this approach

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