Order Pair | AMC-10B, 2012 | Problem 10
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
Algebra
Order Pair
Multiplication
Check the Answer
But try the problem first...
Answer: \(78\)
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 $\frac{M}{6}=\frac{6}{N}$=\(9\)
Other useful links
- https://www.cheenta.com/problem-based-on-triangle-prmo-2016-problem-10/
- https://www.youtube.com/watch?v=VLyrlx2DWdA&t=17s