Question

Cersei and Arya were asked by their teacher Nikhil to apply Euclid’s division lemma, to 37 and 7. Cersei and Arya, both being intelligent were quickly ready with their answers.
Cersei: $37=7\times 5+2$
Arya : $37=7\times 4+9$
Which of the following options is true?

• A. Cersei was wrong and Arya was right.
• B. Both Cersei and Arya were right.
• C. Both Cersei and Arya were wrong.
• D. Cersei was right and Arya was wrong

Answer 1

The correct option is D Cersei was right and Arya was wrong

According to Euclid's Division Lemma if we have two positive integers a and b, then there exists unique integers q and r which satisfies the condition $a=bq+r$ where $0\le r<b$.
In Arya's answer,
a=37, b=7, q=4, r=9
But here remainder = 9, which is greater than the divisor $(0\le r<b)$. This makes it a wrong answer.
In Cersei's answer,
a=37, b=7, q=5, r=2
Both quotient and remainder satisfy the condition.