Question

Given the following problem: I am thinking of a number: The number is even The sum of its digits is divisible by 2 The number is a multiple of 11 The number is greater than 20 and less than 78 The number is a multiple of 3 Write a detailed explanation of the solution of the problem using the problem-solving strategy Eliminate Possibilities

a) Subtraction
b) Addition
c) Division
d) Multiplication

Answer 1

The number that fits all the given constraints (even, the sum of its digits divisible by 2, multiple of 11, greater than 20, less than 78, multiple of 3) is 66.

Step-by-step explanation:

The student asked for a solution to a problem with several constraints on the number in question. To find the number, we need to use a problem-solving strategy that involves Eliminate Possibilities. Let's go through the clues given and eliminate numbers that do not fit all the criteria:

• The number is even.
• The sum of its digits is divisible by 2.
• The number is a multiple of 11.
• The number is greater than 20 and less than 78.
• The number is a multiple of 3.

Considering the criteria, let's list the multiples of 11 between 20 and 78: 22, 33, 44, 55, 66, 77. Next, we eliminate the odd numbers, 33 and 55, and 77 because they are not even. Then, we check for multiples of 3 and find that 66 is the only number remaining that fits all criteria.

So, the number that meets all the given conditions is 66.