Guess and Check
Guess and Check is a useful strategy for certain types of problems. It allows one to make a guess, check against the relevant facts in the problem, and refining the guess to get closer to the correct answer. For example, Matthew is 12 years old and his mother is three times as old. How many years must pass before his mother is twice as old? Is the answer 4 years? No, because in 4 years, she would be 40 years old and he would be 16 and 40 is not twice 16. Refine your guess. Is 20 years correct? No, she would be 56 and he would be 32. 56 is not twice 32. Refine your guess ............ and check.
Other Guess and Check Problems appear below.
Here are the other problem solving strategies:
- Look for a Pattern
- Make A Systematic List
- Make A Drawing Or Model
- Simplify the Problem
Day 1 - Barbara has exactly $2.00 in nickels and dimes. She has twice as many dimes as nickels. How many of each does she have?
Day 2 - Mary bought a scarf for $5.00, spent 1/2 of her remaining money on jogging shoes, bought lunch for $2.00 , then spent 1/2 of her remaining money on a CD. She had $10.00 left. How much did she start with?
Day 3 - (a) I'm thinking of a number. If you multiply it by 3, then subtract 5 and finally add 10, you get 20. What number am I thinking of? (b) I'm thinking of a number. If you multiply its square by 3 and then add 9, you get 117. What is that number? (c) I'm thinking of a number. If you subtract 4 from the number, then multiply the result by 3 and then add 5, you get 26. What is that number?
Day 4 - Each check I write costs 10 cents. I also have to pay a flat fee of 25 cents per month. My bank sent me a letter saying the fees were going to change. The new fee is 8 cents for each check and a flat fee of 50 cents/month. The bank said this would be cheaper for me because of the number of checks I write. What is the least number of checks I must write to make the new fees cheaper?
Day 5 - There are two rectangles whose perimeter is the same number as its area. Find both rectangles.
Day 26 - In a geometry course the grade is based on six tests, each worth 100 points. W. Orrier has an average of 88.5 on his first four tests. What is the lowest average he could obtain on his next two tests and still receive an average of 90 or better?
Day 27 - A Super Notebook was on sale last week at 15 % off the regular price. Then an additional 10 % of the sale price was deducted to give a final super sale price of $ 25.09. What was the regular price of the notebook?
Day 28 - Pythagoras discovered amicable or "friendly" numbers. Two positive integers are amicable if each is the sum of the proper divisors of the other. 284 is amicable with 220. What number is amicable to 1184?
Day 29 - If 100 bushels of corn is distributed so that each man receives 3 bushels, each woman 2 bushels, and each child 1/2 bushel, how many men, women and children are there?
Day 30 - My license tag is a three-digit number. The product of the digits is 216, and their sum is 19 and the digits appear in ascending order. Find the license plate number.
Day 51 - A two-digit number is divided by the sum of its digits. What is the largest attainable remainder?
Day 52 - Remove three of these 15 line segments and leave three squares.
Day 53 Remove six of these 24 line segments to leave three squares.
Day 54 - A girl had her monthly allowance doubled, next received an additional $ 3 increase, and then had her allowance cut in half. How much more or less is her present allowance compared with her original allowance?
Day 55 - A stock market analyst sold a monthly newsletter to 500 subscribers at a price of $ 10 each. She discovered that for each $0.25 increase in the monthly price of the newsletter, she would lose 2 subscriptions. For what price should she sell each issue to bring in the greatest total monthly income?
DAy 76 - Using four - 4's and no other number and any mathematics operation symbol, write an expression whose value is 19. For example, 44/4 + 4 = 15
Day 77 - Find three consecutive odd integers whose sum is -3.
Day 78 - Write the number 1 using each of the nine digits, 1, 2, 3, 4, 5, 6, 7, 8, and 9 only once.
Day 79 - Place parenthesis to make this statement true: 9 x 5 + 2 - 8 x 3 + 1 = 22
Day 80 - How can you place 21 marbles in four boxes so that each box contains an odd number of marbles?
Day 101 - In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. How many cows are there?
Day 102 - Determine the three values of x so that x2 = 2x.
Day 103 - Determine all the values of x and y so that x/y, x times y, and x - y are all equal.
Day 104 - Place the numbers 1 through 10 in the blanks so that any number is the absolute value of the two numbers directly above it.
Day 105 - Using the digits in 1996 and any mathematical operation, generate the numbers 1 through 20. For example, 19 - 9 + 6 = 16.
Day 126 - The operation @ is defined as a @ b = a2 + 3b. Find four pairs of natural numbers such that a @ b = 37
Day 127 - How can you have $ 2 in nickels , dimes, and quarters, with the same number of each coin?
Day 128 - Place the numbers 2, 3, 4, 5, 6, 7, 8, 9 and 10 in the boxes so that the sum of the numbers in the boxes of each of the four circles is 27.
Day 129 - A mathematics teacher's son will be x years old in the year x2 In what year was he born?
Day 130 - Use exactly three - 3's and any nonnumerical mathematical symbols ( i.e. +, -, x, /, sq. rt., etc.) to write expressions that equal each of the numbers one through ten inclusive.
