Discussion
The difference between the remainder obtained on dividing 2002 by 101 and dividing 2201 by 102 lies between :
Answer: B
The difference is 24, which lies between 20 and 25.
Find each remainder:
\[ \begin{aligned} 2002 &= 101 \times 19 + 83 \\ 2201 &= 102 \times 21 + 59 \\ 83 - 59 &= 24 \end{aligned} \]
Check: \(101 \times 19 = 1919\) and \(2002 - 1919 = 83\), which is less than 101; \(102 \times 21 = 2142\) and \(2201 - 2142 = 59\), which is less than 102.
24 is in the range 20 to 25, so the other ranges are wrong. Using quotients 20 and 22 by mistake would give negative remainders, a sign the division has gone one step too far.
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