So we were doing the Gauss Math Contest (no worries, Im not cheating, back home to have lunch). So the Last qustion was this:
In a garden, the gardener opens Tap A and Tap B to fill his pool with water. That took 6 hours. The length of time of one of the Tap fill the pool indivisually would be x. How many possibilities are x (now obviously it doen't matter if it's Tap A or B,)?
Choices a) 5 b) 6 C) 9 d) 10 e)12
This may seems very easy to many people out there., but if one of you can Help Me, I would really appreciate your help
P.S. I was able to come up with only 12hr&12hr for the taps, OH yeah, only "positive interger" hours (e.g. 3 hr, not 3 1/4 hrs)
Here are my ideas :
1. I don't know if this counts as algorithms, but knowing the squares of numbers under 20 could be very helpful (like
Anakin had said), especially in the Pythagorean Theorem. Say you memorized 19², then immediately you may tell that
19x38 is 722 (19^2=361, 361*2=722)
2.Thing like 33*27 equals to (11*3)*(3*9)=11*81=891 Rearranging factors.
3. In addition, try to match up numbers that makes a multiple of 10 (like tidy numbers, you said)
4. For a multiplication of 11: (say 11x44) first write down the left-most digit, (i.e. the 4) then write down the sums of adjacent numbers starting from the left-most digit. (e.g., thousand+ hundreds, hundreds+tens, tens+ones)and stop after calculating the tens digit and the ones digit. If any of the sums exceeds 9, add 1 to the previous sum. So now we have 48_
Finally, write down the ones digit. so 44*11 =484 in the same way, 11x34=374, 11x345=3795, 11x765=8415. This may be confusing, and useless but just interesting to point out (and the fact is that you probably know this already).
5. At the last, I say, practise will make anyone better and faster at almost anything. If you practise enough times, you can just tell the anwser without pondering. Just practise and you might find some neat strategies of arithmetic
Thank you for your assistance as well as your patience
Just last night (in bed, before reading your explanation) I was thinking and I found :
for 2x = 5y ==> 1x=2.5y==> 1y= 0.4x ===> x+y=1.4x
Lowest multiple of 1.4 is 7 then yeah.....
a slight variation of your second method, basically
Just, like, sharing ideas if you don't mind.
The 1st is really helpful, not that the 2nd one isn't, Thank you
'Night, See you around
Hi guys, here is the question:
The integer numbers x and y satisfy the equation 2x=5y
Only 1 of the following can be the sum of x and y
2012, 2011, 2010, 2009, 2008
The standard anwser is 2009. The question is why??
Any thought might be a helpful hint to others.