Question

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Given: x = 5 ( mod 13 )
Which of the following integers are valid solutions for x ?
Choose all answers that apply:


(Choice A)
A
-21

(Choice B)
B
5

(Choice C)
C
17

(Choice D)
D
29

(Choice E)
E
31

(Choice F)
F
None of the Above

Answer 1

Choice B : 5

Explanation:

The question belongs to modular arithmetic. When two integers are divided , we get an equation like:

A/B=Q remainder R

Sometimes, the remainder is more important. For that purpose, we use “mod” (Modulus operator)

The modulus operator gives us the remainder when two integers are being divided i.e. if we have an expression like

14 mod 6= ?

We will get the answer, the remainder as 2.

So for the given question,

x=5 (mod 13)

As the number that is being divided by 13, a number greater than the divisor, the quotient will be zero and the remainder will be 5.

So

x=5

So choice B is the correct answer.