We have: \(\dfrac{1}{20}+\dfrac{1}{12}=\dfrac{2}{15}\)

=> m = 20; n = 12.

=> m+n = 20+12 = 32.

So the answer is: 32

We have: \(a\ge b\ge c\ge d\ge e\)

=> \(d+e=110;a+b=121\)

We have: \(110+112+113+114+115+116+117+118+120+121=4\left(a+b+c+d+e\right)\)

\(=\Sigma S\) (1)

<=> \(289=a+b+c+d+e\)

<=> \(289-\left(a+b\right)-\left(d+e\right)=c\)

<=> \(c=289-110-121=58\)

From (1)

=> \(121>S\ge116\) (corespond to: \(\left(c,a\right)\)) (2)

From (2) => The largest number is: \(a=120-58=62\)

Dao Trong Luan, you missed: \(a+b=77\)

And the answer is: 77.

The probability of the girl in the twins go to the district championship is: \(3:8=\dfrac{3}{8}\)

The probability of the girl in the twins go to the district championship is: \(3:6=\dfrac{1}{2}\)

So their probability is: \(\dfrac{3}{8}\cdot\dfrac{1}{2}=\dfrac{3}{16}\)

Since \(A\cap B=\left\{1\right\}\), then we need to calculate the number of ordered pairs from the numbers: 2;3;4;5;6;7;8;9;10

(1)If the contents in one set is 1 => There are 9 ordered pairs

(2)If the contents in one set is 2 => There are 8*7 ordered pairs

(3)If the contents in one set is 3 => There are 7*6*5 ordered pairs

(4)If the contents in one set is 4 => There are 6*5*4*3 ordered pairs

Call all the ordered pairs in (1)(2)(3)(4) B. Reverse the sets we have the number of ordered pairs = B*2.

So there are: \(\left(9+8\cdot7+7\cdot6\cdot5+6\cdot5\cdot4\cdot3\right)\cdot2=1270\left(order-pairs\right)\)

We have: \(991+993+995+997+999=5000-N\)

\(4975=5000-N\)

\(N=5000-4975=25\)

Choose E

We have: \(D=1\cdot2\cdot3+2\cdot3\cdot4+...+20\cdot21\cdot22\)

\(4D=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot4+...+20\cdot21\cdot22\cdot4\)

\(4D=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(4-1\right)+...+20\cdot21\cdot22\cdot\left(23-19\right)\)

\(4D=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+20\cdot21\cdot22\cdot23-19\cdot20\cdot21\cdot22\)

\(4D=20\cdot21\cdot22\cdot23\)

\(D=\left(20\cdot21\cdot22\cdot23\right):4\)

\(D=53130\)

The distance A rode is: 60 - 12 = 48 (km)

The distance B rode is: 60 + 12 = 72 (km)

The ratio of the speed of A-B is: 48:72 = 2:3

So the rate of speed of A was: 4*2 = 8 (km/h)

Choose B

The maximum product of the positive integers is: \(2\cdot3\cdot4\cdot5\cdot6=720\)

So the answer is: 720.

You don't need any material, just need a mathematic book to study and rest.

P/s: + This is my opinion. This is advice question, not maths question.

       + This question is asked 2 times.

The analog clock will show right the time after it loses 12 hours.

We have: 12 hours = 720 minutes.

The clock will show the correct time after: \(\left(720:2\right)\cdot3=1080hours=45days\).

This is the shortest correct answer, so the answer you gave is not correct.

We have 4 sets of A: 

\(A=\left\{1;2;3\right\}\)or \(A=\left\{1;2;4\right\}\) or \(A=\left\{1;3;4\right\}\) or \(A=\left\{2;3;4\right\}\)

We have: 25 < 27 < 81 < 243 < 250

<=> \(25< 3^3< 3^4< 3^5< 250\)

\(n\in\left\{3;4;5\right\}\)

15m/s = 0.015km/s = (0.015*60)km/h = 54km/h

Sorry, but there isn't enough information to answer.

We have: \(240984\times234=56390256\)

=> \(a=9;b=3\)

Because \(\left|x\right|\ge0\)

We have:\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=5x\) 

<=> \(x+1+x+2+x+3+x+4=5x\)

<=> \(4x+10=5x\)

<=> \(10=5x-4x\)

<=> \(10=x\)

So the only answer satisfy is: \(x=10\). Dao Trong Luan's answer was not correct

We have: \(5^n=...5\)

=> \(A=...5+...5+...+...5\left(100-factors\right)\)

We have: \(...5\left(2n-factors\right)=...0\)

=> \(A=...0\)

So the last digit of A is: 0

Sorry, the name is Phan Thanh Tịnh. Go to the history and figure it by yourself.

Oh, I was wrong! Thanks Dao Trong Luan and Kaya Renger :)