Mathcounts
Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:11
Nguyễn Mạnh Hùng 25/06/2018 at 07:46
In the sequence, a must be the first number in the sequence and d must be the distance
We have: 10 = 1+9 = 2+8 = 3+7 = 4+6 = 5+5
So there are 10 pair of (a;d) counting the conversion
It's not sure yet ^^
Lê Quốc Trần Anh selected this answer.
Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:10Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:09Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:09Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:09Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:08
Nguyễn Mạnh Hùng 26/06/2018 at 02:15
The number of alcohol in the first is:
400 x 64% = 256 (kg)
=> There are 144 kg of water
When drained 100kg of the mixture or drained 25% of the mixture and replaced by 100kg of water, the total kg of the tank don't change.
The alcohol left is: 256  256 x 25% = 192 (kg)
The water is: 144  144 x 25% + 100 = 208 (kg)
After two steps, the water is: 208  208 x 25% + 100 = 256 (kg)
After three steps, the water is: 256  256 x 25% + 100 = 292 (kg)
=> The alcohol is: 400  292 = 108 (kg)
=> The percent is: 108 / 400 = 27% of the tank
Lê Quốc Trần Anh Coodinator
06/04/2018 at 11:10
¤« 07/04/2018 at 14:39
The difference between the loud rock concert and the normal conversation is 12060=60 dB. It's 3 times of 20 dB. Because every increase of 20 dB corresponds to sound becoming 10 times as loud, the rock concert must be 10 × 10 × 10 = 1000 times as loud as the normal conversation.

FC Alan Walker 07/04/2018 at 04:25
The difference between the loud rock concert and the normal conversation is 12060=60 dB. It's 3 times of 20 dB. Because every increase of 20 dB corresponds to sound becoming 10 times as loud, the rock concert must be 10 × 10 × 10 = 1000 times as loud as the normal conversation.
Lê Quốc Trần Anh Coodinator
06/04/2018 at 11:10
¤« 07/04/2018 at 14:39
April has 30 days.
=> Zeus needs to throw: 30.12=360 (lightning bolts) in April.
In the first week of April, he has thrown: 15.7=105 (lightning bolts)
In the next 307=23 days, Zeus needs to throw: 360105=255 (lightning bolts)
So the average is: 255:23=11.08≈
11 (lightning bolts per day).

FC Alan Walker 07/04/2018 at 04:15
April has 30 days.
=> Zeus needs to throw: 30.12=360 (lightning bolts) in April.
In the first week of April, he has thrown: 15.7=105 (lightning bolts)
In the next 307=23 days, Zeus needs to throw: 360105=255 (lightning bolts)
So the average is: 255:23=11.08\(\approx\)11 (lightning bolts per day).
Lê Quốc Trần Anh Coodinator
06/04/2018 at 11:09
FC Alan Walker 07/04/2018 at 04:20
In each day, Gaylon uses 8 digits. We have: 2018:8 = 252 and the remainder is 2. The 253rd day of the year is in September, so Gaylon writes the first two digits of the number is 09 in the month of September. The 2018th digit he writes down is 9.