Required Mathematical Intelligence

Chapter 47 Jam
A mail order company sells jams.There are three cans of jam in each box, and the jam has five flavors: grape, orange, strawberry, peach, and apple.Each jar of jam contains only one flavor.Boxes must be packed according to the following conditions:
1. Each box must contain two or three different flavors;

2. A box containing orange marmalade must contain at least one jar of grape marmalade;
3. There must be at least one jar of orange marmalade in a box containing grape marmalade;
4. Peach jam and apple jam cannot be packed in the same box;

5. A box containing strawberry jam must contain at least one jar of apple jam; however, a box containing apple jam does not necessarily contain strawberry jam.

problem:

Question 1 Which of the following boxes of jams meets the conditions of the question?

(A) A jar of peach jam, a jar of strawberry jam, and a jar of orange marmalade;
(B) A jar of orange marmalade, a jar of strawberry jam and a jar of grape jam;
(C) Two jars of strawberry jam and one jar of apple jam;
(D) Three jars of peach jam;
(E) Three jars of orange marmalade.

Except for one case in question 2, each of the following boxes meets the conditions of the question.This situation is:

(A) grape jam and peach jam;

(B) peach jam and apple jam;

(C) Orange marmalade and peach marmalade;

(E) Strawberry jam and apple jam.

Question 3 Which of the following boxes can meet the conditions of the question after adding a can of strawberry jam?

(A) A jar of peach jam and a jar of orange marmalade;
(B) a jar of grape jam and a jar of orange marmalade;
(C) Two jars of apple jam;
(D) Two cans of orange marmalade;
(E) Two jars of grape jam.

Question 4 A can of orange marmalade, a can of peach jam, plus a can of what jam can make a box?
(A) grape jam;
(B) orange marmalade;
(C) strawberry jam;
(D) peach jam;
(E) Apple jam.

Question 5 A can of orange marmalade and which two of the following cans of jam can make a box?
(A) A jar of orange marmalade and a jar of strawberry jam;
(B) A jar of grape jam and a jar of strawberry jam;
(C) Two cans of orange marmalade;
(D) Two jars of grape jam;
(E) Two jars of strawberry jam.

Question 6 Which of the following two cans of jams cannot be contained in a box of qualified jams?

(A) A jar of strawberry jam and a jar of peach jam;
(B) a jar of grape jam and a jar of orange marmalade;
(C) Two cans of orange marmalade;
(D) Two jars of grape jam;
(E) Two jars of strawberry jam.

Question 7 A box of qualified jams cannot contain the following two jars of jams?
(A) orange marmalade;
(B) grape jam;
(C) apple jam;
(D) strawberry jam;
(E) Peach jam.

[Answer: Answer 1 choice (A) violates both the known condition 2 and the known condition. Hole choice (B) violates the known condition 5. Choices (D) and (E) both violate the known condition 1. Therefore, it should Choose (C).

Answer question 2 and you should judge immediately: choose (B).Because (B) violates known condition 4.

Answer 3 choices (C).Choice (A) violates known conditions 2 and 5. According to known condition 5, choice (B) is not acceptable.If the box contains strawberry jam, it must contain apple jam, plus grape jam and orange jam, and there will be more than three types of three-naan jam in this box.This violates the meaning of the question and the known conditions.Choices (D) and (E) will both produce problems similar to those of choice (B).For similar questions like this, you can directly find apple jam based on known condition 5, so that you can improve the speed of doing the questions.

答题4选（A），由橘子果酱、桃子果酱、葡萄果酱装成一箱符合所有的题设条件。选（B）和（D）违反已知条件2.选（C）违反已知条件认2、4、5.选（E）违反已知条件2、4.
Answer 5 choices (D).According to known condition 2, only (B) and (D) may be right, and (B) violates known conditions 5, 1 and the condition of the question, so only (D) can be selected.

Answer 6 choices (A).Because according to known condition 5, strawberry jam must contain apple jam, and according to known condition 4, apple jam and peach jam cannot be packed in the same box at the same time.According to known condition 5, strawberry jam and peach jam cannot be packed in the same box.

Answer 7 choices (E).The reason is that two jars of peach jam, or one jar of orange jam, or one jar of apple jam, or one jar of grape jam, or one jar of strawberry jam, would violate the condition of the problem.If you add a jar of orange marmalade, you need to add a jar of grape jam.If you add a jar of grape jam, you need to add a jar of orange marmalade.If you add a jar of apple jam, you obviously violate the known condition 4. If you add a jar of strawberry jam, then add another jar of apple jam.Therefore, one box cannot contain two jars of peach jam. ]
(End of this chapter)