Try this beautiful problem from Algebra: Order Pair

Order Pair – AMC-10B, 2012- Problem 10

How many ordered pairs of positive integers (M,N) satisfy the equation $\frac{M}{6}=\frac{6}{N}$

  • \(31\)
  • \(78\)
  • \(43\)

Key Concepts


Order Pair


Check the Answer

But try the problem first…

Answer: \(78\)

Suggested Reading

AMC-10A (2010) Problem 21

Pre College Mathematics

Try with Hints

First hint

Given that $\frac{M}{6}=\frac{6}{N}$ \(\Rightarrow MN=36\).Next we have to find out the the Possibilities to getting \(a \times b=36\)

can you finish the problem……..

Second Hint

Now the possibilities are ….

$1 \times 36=36$
$2 \times 18=36$
$3 \times 12=36$
$4 \times 9=36$
$6 \times 6=36$

We can reverse the order of the factors for all of the ones listed above, because they are ordered pairs except for 6*6 since it is the same back if you reverse the order.

can you finish the problem……..

Final Step

Therefore the total Possible order pairs that satisfy the equation $\frac{M}{6}=\frac{6}{N}$=\(9\)

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