Chapter 3: Problem Solving And Reasoning Problem Set

Chapter 3: Problem Solving And Reasoning Problem Set.

1. Three people are lined up behind each other, from shortest to tallest. They are shown five hats, three blue, and two red. The people are blindfolded and placed on their heads. The two extra hats were kept, and the blindfolds were removed. All of them were asked if they knew what hat they were wearing, starting from the tallest. The tallest and the middle person both answered that he knows. How did he know and what color is the hat he is wearing..

STEP 1: UNDERSTAND THE PROBLEM. -How did the tallest and middle person know the color of their hats.

STEP 2: MAKE A PLAN. a) 3 people are lined up behind each other, from smallest to tallest.

If the hat of the middle person is color… If the hat of the smallest person is color… Then the possible color of the hat of the tallest person are… Blue Red Blue, Blue, Red Blue = 66.67% Red = 33.33% Red Blue Red, Blue, Blue Blue = 66.67% Red = 33.33% Blue Blue Blue, Red, Red Blue = 33.33% Red = 66.67% Red Red Blue, Blue, Blue Blue = 100% Red = 0%.

*From the statement (d), the reason why the tallest person knew the color of the hat he is wearing is that he saw the middle and smallest person are wearing red hats. Since there are only 2 red hats, then it is given that his hat is blue..

STEP 4: LOOK BACK AT THE PROBLEM. Therefore, the tallest person knew the color of his hat, since he saw that the middle and smallest person wearing red hats. Giving him the hint that his hat can only be color blue since there are only 2 red hats. The middle person also answered that he knew the color of the hat he is wearing since he can see the hat of the smallest person which is red and basing it to the answer of the tallest person, he knew that he is also wearing a red hat..

2. If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours?.

UNDERSTAND THE PROBLEM. 2. If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours?.

3. CARRY OUT THE PLAN (SOLUTION). .

. We need the x to be left alone so we need to divide both sides by 4. Multiply 8 and 6 product will be divided by 4..

3. Find the unit digit for the sum 13 25 + 4 81 + 5 411.

UNDERSTAND THE PROBLEM. Finding the unit digit is required by the problem, but first we must understand what a unit digit is..

3. CARRY OUT THE PLAN (SOLUTION). Step 1 . Find the unit digit of 13 25.

Step 2. Find the unit digit of 4 81. 41=4. 42=16.

Step 3. F ind the unit digit of 5 411. 51=5. 52=25.

Step 4 . Add the unit digit of 13 25 + 4 81 + 5 411.

4. An egg vendor broke all eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7 , he had none left over. What is the smallest number of eggs he could have had in the shipment?.

Get the LCM of 4, 5, and 6. (2 and 3 are canceled as 4 and 6 represent them.) Option 1 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 52, 56, 60 5 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 6 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 LCM= 60.

Option 2 (technique) 2 4 5 6 2 2 5 3 3 1 5 3 5 1 5 1 1 1 1 (2)(2)(3)(5)= 60.

Solve for package 7 We will be using 60n + 1 where n is all real numbers and 1 is the remainder of packages 2, 3, 5, and 6. The answer 60n + 1 should be divisible by 7. N= (1, 2, 3, 4, 5,…n) 60(1) + 1 = 61 61/7 = 8.71 60(2) + 1 = 121 121/7 = 17.42 60(3) + 1 = 181 181/7 = 25.86 60(4) + 1 = 241 241/7 = 34.43 60(5) + 1 = 301 301/7 = 43 60(12) + 1 = 721 721/7 = 102 60(19) + 1 = 1140 1141/7 = 163.

5. There are 1000 lockers in a high school with 1000 students. The first students opens all 1000 lockers; next, the student closes lockers 2, 4, 6, 8, 10, and so on up to locker 1000; the third student changes the state ( opens lockers that are closed and closes lockers that are open) of lockers 3, 6 ,9 ,12, 15, and so on; the fourth student changes the state of lockers 4, 8, 12, 16, and so on. This continues until every student has had their turn. How many lockers will be open at the end?.

STEP 1: UNDERSTANDING THE PROBLEM. The problem requires us to analyze the pattern of the 1000 lockers with 1000 students..

Step 2: MAKING A PLAN. Let us use a table, containing 15 students and 15 lockers..

STEP 3: CARRYING OUT THE PLAN. ➢Each student opens and closes only their lockers that are multiple of their number..

STEP 4: LOOKING BACK. ➢Perfect squares always have an odd number of factors..

6. Solve the given Ken-Ken Puzzle. 16X 12X.

STEP 1 UNDERSTANDING THE PROBLEM. The ken-ken puzzles is 4x4 , thus, the numbers inside must only be from 1-4..

abstract. A picture containing table. 6. Solve the given Ken-Ken Puzzle.

abstract. A picture containing table. 6. Solve the given Ken-Ken Puzzle.

A picture containing table. 6. Solve the given Ken-Ken Puzzle.

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