Question

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

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

Answer 1

The correct option is D Cersei was right and Aryan 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 Aryan'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.