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STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS)
CLUSTER 1/STANDARD 1

SAMPLE TEST QUESTION

Standard 1, Strand A (0pen-ended)

Find all of the numbers that satisfy the following statements:

1. I am a positive integer less than 100.
2. Two more than my value is a multiple of 6.
3. The sum of my digits is a multiple of 7.

Show all of your work and explain the process you use to find the solution completely.

Reprinted with permission from the Mathematics Teacher.
Copyright May 1997 by the National Council of Teachers of Mathematics.
All rights reserved.

Rationale:

From statement 1, we have the positive integers less than 100, i.e., 1, 2, 3, 4, …, 98, 99.

From statement 2, we conclude the number is two less than the multiples of 6 that are less than 100. The following numbers are multiples of 6 less than 100: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96. The number you are looking for, therefore, is from among the following list: 4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, and 94.

From statement 3, the sum of the digits in the number is a multiple of 7. The numbers 16, 34, 52, and 70 are responses that meet all the criteria given.