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1. Look! The car is moving so fast.
2. Listen! Someone is whispering in the next room.
3. Is your friend sitting next to the beautiful girl over there at present?
4. Now Joy is trying to pass the examination.
5. It’s 11 o’clock, and my mom is cooking lunch in the kitchen.
6. Keep silent! You are singing so loudly.
7. I am not staying at home at present.
8. Now Hana is lying to her mother about her bad marks.
9. At present they are traveling to LA.
10. Jim is not working in his office now.
\(#FallenAngel\)
1 Which planet is the biggest in our solar system?
2 He is the worst doctor I've ever known.
3 She is the happiest woman in our office.
4 This is the most boring film I've ever seen this week.
5 We have many books, but this is the most interesting one.
6 We have many subjects, but I think English is the most important.
7 That is the cheapest hat in our shop, Madam.
8 She is the best singer in America.
9 Maths is the most difficult for me. I like English and Art.
10 He is the most careful student in our school.
1 the biggest
2 the worst
3 the happiest
4 the most boring
5 the most interesting
Dịch đề: Cho dãy số 2, 7, 12, 17, 22, 27,..., 302, 307. Tìm chữ sồ hàng đơn vị của tích tất cả các số trong dãy.
Solution (in English):
In the sequence, there are \(\left(302-2\right):10+1=31\) numbers that end with 2 and \(\left(307-7\right):10+1=31\) numbers that end with 7.
Therefore, the unit digit of the product is also the unit digit of:
\(A=2\times2\times2\times...\times2\times7\times7\times7\times...\times7\)
(31 numbers 2) (31 numbers 7)
We have to find out what is the final digit of \(2\times2\times...\times2\) (31 times) and \(7\times7\times...\times7\) (31 times)
Consider the number \(N=2\times2\times...\times2\) (\(n\) times)
If \(n=1\), then \(N=2\)
If \(n=2\), then \(N=4\)
If \(n=3\), then \(N=8\)
If \(n=4\), then \(N=16\rightarrow\) the last digit is 6
If \(n=5\), then \(N=32\rightarrow\) the last digit is 2
If \(n=6\), then \(N=64\rightarrow\) the last digit is 4
If \(n=7\), then \(N=128\rightarrow\) the last digit is 8.
If \(n=8\), then \(N=256\rightarrow\) the last digit is 6.
...
From here we can see a pattern: If \(n\) has a remainder of 3 when being divided by 4, the last digit of N is 8. Thus, the final digit of \(2\times2\times...\times2\) (31 times) is 8 since 31 has a remainder of 3 when being divided by 4.
Using the same method of reasoning, we can deduce that \(7\times7\times...\times7\) (31 times) ends with 3.
Therefore, the final digit of A must be the final digit of \(8\times3=24\), which is 4.
So the answer is 4.
Which class are you in?
How many rooms does your house have?
How many people are there in your family?
Where is your house?
What time is it?
Which class are you in?
- I'm in class 6/1
How many rooms does your house have?
- My house has three rooms.
How many people are there in your family?
- There are five people in my family.
Where is your house?
- My house is in the city.
What time is it?
- It's half past nine.
\(#FallenAngel\)
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