Hai số tự nhiên A và B, biết A < B và hai số có chung những đặc điểm sau:

- Là số có 2 chữ số. 

- Hai chữ số trong mỗi số giống nhau. 

- Không chia hết cho 2 ; 3 và 5. 

a) Tìm 2 số đó. 

b) Tổng của 2 số đó chia hết cho số tự nhiên nào ?

Số dư của phép chia 172869 : 345 là:

A. 31

B. 24

C. 42

D. 21

Cho phương trình x 3 − 2 m + 1 x 2 + 4 m − 1 x − 2 m + 1 = 0 . Tìm m để phương trình có một nghiệm duy nhất?

A.  m ∈ ∅

B.  m = 0

C.  m = 1

D. m=2

Reflexology is a natural treatment dating back to ancient times. It is based on the idea that there are zones, or areas, in the feet and hands that are related to other parts and systems of the body. For example, the tips of the toes or fingers are related to the head and neck, and the ball of the foot is related to the heart and chest. A reflexologist applies pressure to specific areas in a patient’s feet and hands to relieve symptoms or pain in other related areas.

This type of treatment does not cure or diagnose specific health problems, and it does not involve any medication. Yet many patients find that it successfully relieves symptoms of stress and disease. Reflexology is effective for pain, headaches, and sleeping difficulties, among other ailments. Applying pressure to the feet and hands relieves tension, improves blood circulation, and relaxes muscles. It promotes the natural, healthy functions and well­being of the entire body. Reflexology is often used along with other types of treatments, including conventional medicine.

This gentle therapy is safe and simple. A reflexologist’s only tools are his or her hands. Pressure is strong, but not uncomfortable. It’s not uncommon for patients to fall asleep during treatments.

A typical treatment session lasts one hour. Treatment is usually focused on the feet for most of the session. A patient is asked to remove his or her shoes and socks, to sit in a comfortable reclining chair, and then to relax as the reflexologist warms the patient’s feet with his or her hands and applies pressure to the appropriate parts of the foot. The last ten minutes of the session are dedicated to the hands.

After relieving specific problems, many patients continue a regular programme of treatment to maintain good health. Some reflexologists suggest building at least a five- minute reflexology session into every day for long-term relief of stress and pain.

In order to have good effect , we should____.

A. have a long-term relief session combined with medicine

B. remove our shoes and socks every day

C. have a regular five-minute reflexology session every day

D. try to avoid specific problems in our daily life

Tập hợp  ( − 4 ; 3 ] ∩ ℤ bằng tập nào dưới đây?

A.  { − 3 ; − 2 ; − 1 ; 0 ; 1 ; 2 ; 3 }

B.  { − 4 ; − 3 ; − 2 ; − 1 ; 0 ; 1 ; 2 ; 3 }

C.  { − 3 ; − 2 ; − 1 ; 0 ; 1 ; 2 }

D.  { 0 ; 1 ; 2 ; 3 }

Cho tứ diện ABCD có AB = AC = AD; góc BAC bằng góc BAD bằng 60 o . Gọi M và N là trung điểm của AB và CD

Kết luận nào sau đây sai?

A. MN vuông góc với AB

B. MN vuông góc với CD

C. MN vuông góc với AB và CD

D. MN không vuông góc với AB và CD