Assertion (A): 1000 ≡ -1 (mod 7). Reason (R): 7 divides 1001.

Modulo Arithmetic & Congruence · Question 51 of 97

Question 51

MediumOriginal question

Assertion (A): $1000 \equiv -1 \pmod{7}$ .
Reason (R): 7 divides 1001.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$1000 - (-1) = 1001 = 7 \times 143$ .
So both are true, and R is exactly the reason A holds.

Concept: Congruence to a negative number
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsCongruence modulo n

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Assertion (A): 1000≡−1(mod7)1000 \equiv -1 \pmod{7}1000≡−1(mod7).Reason (R): 7 divides 1001.

Explanation

Assertion (A): $1000 \equiv -1 \pmod{7}$ .
Reason (R): 7 divides 1001.