How many two-digit prime numbers have a remainder of 2 when divided by

Question

How many two-digit prime numbers have a remainder of 2 when divided by 7?

A. none
B. one
C. two
D. three
E. more than three

LevanKhukhunashvili · Accepted Answer

As I don't know any possible shortcut, Hello "Brute Force", my old friend.

So we need 7*n+2=must be two digit prime, n is a non zero integer
We can exclude n=even as even+even=even and even two digit integer cant be prime

So let's see
7*3+2=23 (Drop A)
7*5+2=37 (Drop B)
7*7+2=51 divisible by 3
7*9+2=65 not a prime
7*11+2=79 (Drop C)
7*13+2=93 divisible by 3
7*15+2=107 not a two digit integer

IMO
Ans:  D

CareerGeek · Answer

Two digit prime numbers are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97
Remainders when divided by 7 are

11 --> 4
13 --> 6
17 --> 3
19 --> 5
 23 --> 2 
29 --> 1
31 --> 3
 37 --> 2 
41 --> 6
43 --> 1
47 --> 5
53 --> 4
59 --> 3
61 --> 5
67 --> 4
71 --> 1
73 --> 3
 79 --> 2 
83 --> 6
89 --> 5
97 --> 6

IMO Option D.

Pls Hit Kudos if you like the solution

Bunuel  Is there any shortcut for this question ? Thanks

Fdambro294 · Answer

Anyone think of a creative method other than brute force?

I brute forced this one too.

Posted from my mobile device

MathRevolution · Answer

Let's focus on table 7.

The first digit is 7 * 1 = 7 and the last two-digit that 7 will contain is 98.

7 * even number will not be a prime. Hence, we are left with only 7 * odd numbers.

Now to be it a prime with remainder of 2 , we have possibilities as 21 + 2 = 23, 35 + 2 = 37 and 77 + 2 = 79.

Answer D

BrushMyQuant · Answer

How many two-digit prime numbers have a remainder of 2 when divided by 7?

Dividend = Divisor * Quotient + Remainder

=> n (number) = 7*k + 2 (where k is the quotient) = 7k + 2

When k is even then we will have n as even => they will not be prime
So, lets focus on the odd values of k

k = 3, n = 7*3 + 2 = 23 ->   PRIME  
 k = 5, n = 7*5 + 2 = 37 ->   PRIME   
 k = 7, n = 7*7 + 2 = 51 ->   NOT PRIME   
 k = 9, n = 7*9 + 2 = 65 ->   NOT PRIME   
 k = 11, n = 7*11 + 2 = 79 ->   PRIME   
 k = 13, n = 7*13 + 2 = 93 ->   NOT PRIME   
 k = 15, n = 3 digit number

this video  to  MASTER how to find Prime numbers between 1 to 100  ]

=> Three values 23, 37, 79

So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

How many two-digit prime numbers have a remainder of 2 when divided by

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How many two-digit prime numbers have a remainder of 2 when divided by

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