1969 AHSME Problems/Problem 24

Problem

When the natural numbers $P$ and $P'$ , with $P>P'$ , are divided by the natural number $D$ , the remainders are $R$ and $R'$ , respectively. When $PP'$ and $RR'$ are divided by $D$ , the remainders are $r$ and $r'$ , respectively. Then:

$\text{(A) } r>r' \text{ always}\quad \text{(B) } r<r' \text{ always}\quad\\ \text{(C) } r>r' \text{ sometimes and } r<r' \text{ sometimes}\quad\\ \text{(D) } r>r' \text{ sometimes and } r=r' \text{ sometimes}\quad\\ \text{(E) } r=r' \text{ always}$

Solution

$\fbox{E}$

1969 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35
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1969 AHSME Problems/Problem 24

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